Transcript for:
Lecture on Logarithms, Antilogarithms, and pH Calculation

good evening children this is our lakshmi r n and before starting the class let us initiate the class with the one minute prayer let us start the prayer thank you children kindly all of you vibrate the words i will clearly do the good score i will also pray for you all three times okay you children today's uh point of interest or the topic of interest is logarithm and anti-logarithm table how to use how to do calculations using log and antilog tables that is number one number two extending the same concept idea or applying the same idea to your ph calculation that is the idea okay now let us discuss before going to ph calculation let us discuss the idea of log and anti logarithm table log and anti logarithm table of course when i say logarithm and added algorithm table this is basically with respect to your corresponding to the base 10 logarithm we have got two fundamental table one is to the base 10 the other one is to the base e and to the base e is called as natural logarithm whenever i say logarithm of x this implies logarithm of x to the base ten when we say log x it is logarithm of x to the base ten log of x to the base e is also understood as natural logarithm of x simply l n x l n x l n x is nothing but log of x to the base e and e is nothing but your corresponding euler's constant and whose value is 2.71 something etcetera let us not worry about that now log x is nothing but log of x to the base 10. now in this table how to handle the table how to use the table to find the log values and anti log values children suppose if we have a calculation you are 100 divided by 25 you can directly say 4 you can simply divide and say 4 we have 25 by 100 then you can simply say 1 by 4 the calculations are very simple suppose if you have a calculation you are 13 divided by 131 13 divided by 131 or 13 divided by 181 like this such calculations cannot be directly done with a normal your number of mathematics of course we can divide there is no doubt about it if you are very strong in multiplication and division and use of numbers definitely we can do at least to a certain extent to a certain degree of accuracy we can do but logarithm will give a method the log table or logarithm in mathematics will give a method to understand the value either multiplication or division or whatever may be the quotient it makes us to understand the value up to nearly almost 4 decimals up to nearly almost 4 decimals now let us initiate the discussion with respect to your log table how to understand your logarithm table logarithm table i hope you all will have a table the table may be the clerk's table book or you may have a log sheet like this you may have a log sheet like this and this sheet consists of a corresponding entries and i am going to discuss about the corresponding entries how they are positioned how they are positioned log table consists of three segments segment a segment b and segment c segment a segment b segment c even anti-lock table also consists of three segments segment a segment b segment c what does this segment a in log table refer to segment a refers to our segment a consists of numbers from 10 to 99 from 10 to 99 you can see in the log table it will start from 10 11 12 13 etc it will go up to 99 the vertical column the vertical column may be the first column i would say where the entries 10 11 12 13 up to 54 on one side and from 55 to corresponding 99 on other side that corresponds to what is called as in our language we call as segment a we call as segment a segment a is from 10 to 99 in logarithmic table segment a is 10 to 99 in logarithmic table what does this segment be refer to segment b is will have the corresponding entries from 0 to 9 segment b will have entries from 0 1 2 3 up to 9 and this entry all the entries in this particular segment all the entries in this particular segment corresponds to what is called the segment b this is segment b this is segment b segment a refers to the numbers starting from 10 and ending to what up to 99 under your log table under your log table okay and the segment b will have the entries from 0 to 9 the numbers from 0 to 9 you can see at the top you can see at the top 0 to 9 and that is called as your the corresponding entire block we can call as segment b and what about the corresponding segment c the segment c will have entries from 1 to 9 we call as mean difference we call aside we have the column called mean difference you can see on the right side mean difference it has got entries from 1 to 9 it has got increase from 1 to 9 and each one will have got what corresponding entries in between and that is the idea of three segments in your log table log table consists of three segments one is your segment a having the entries let 10 to 99 segment b having numbers from 0 to 9 and segment c having the numbers from 1 to 9 1 to 9 in a similar manner antilog table also antilog table also antilog table also has the same typical segments segment a segment b segment c segment b and segment c are similar to log table segment b and segment c are similar to log table segment b and segment c are similar to log table what about segment a segment a in anti log will have entries from point zero zero to point nine nine we'll have entries from point zero zero point zero zero point zero one point zero you can see in the antilog table the first column it has point zero zero point zero one point zero two etcetera etcetera up to point four nine and then on the other side point five zero two point nine nine and that entire system of numbers that is the entire system of numbers point zero zero two one point nine nine we commit ourselves or give the name as what the corresponding segment a therefore the only difference between your log table and antilog table is what the first segment values a segment values 10 to 99 with respect to your log table on point zero zero to 0.99 with respect to antilog table whereas the segment b and segment c are one on the same in anti lock table also you can see segment b will have numbers from 0 to 9 and the segment c will have numbers from 1 to 9 and therefore the numbering pattern will not vary with respect to segment b and segment c whereas the numbering pattern varies with respect to what the corresponding segment a which is which has got 1 0 10 to 99 in the case of log table and point 0 0 to 0.9 and in the case of antilog table i hope you all understand children did you all follow the entries about the different segments kindly give your i mean reply so that i will pass on to the next one any one or two it's not that all of you yeah he will take a poll and say thank you mom thank you man please please please they are able to understand the segment then we can proceed further i hope all of all the children should have the corresponding log on anti-log table with you and madam already she had informed she said she had already informed you all i am waiting for the corresponding pole value i think i can go to the next one so i need to clear the board and then go with the next concept okay okay some few children even if they are unable to answer that's fine for me yes thank you thank you thank you man very nice of you so i'll clear the board because some of the children may take may write from the board may take more so i don't want to clear the board without the concern from the student side so that is very very important okay unless and until you give a positive sign we we won't be in a position to do go further okay yeah now coming on to the the next idea yeah so then now we will pass on to how to do how to use the corresponding log table and anti-log table first we will understand the usage of your log table how to use the log table now we are going to find the value of log of one two three four logarithm of one two three four i have chosen the number one two three four how to go with the find how to find the logarithm of one two three four children in logarithm in while taking logarithm please understand please understand that we have to take the first four digit from the left we have to take the first four digit from the left we have to take the first four digits from the left we have to take the first four digit from the left suppose if you have only one two three then you should consider as 123.0 if you have only 12 then you have to consider as 12.00 if you have only one then you have to consider as 1.000 if you have 12.34 uh six seven if you have twelve point three four six seven we want only the first four value we want only the first four value so therefore one two three instead of four the next number is more than five add one year therefore instead of considering one two three four or twelve point three four i'm going to consider 12.35 i'm going to consider 12.35 because logarithm involves only four numbers logarithm involves only four numbers and therefore the first four number we should take from the left the first four numbers we should take from the left the first four numbers we should take from the left first number should not be zero it should be a non-zero the first number should be a non-zero you cannot say sir i can consider zero one two three no zero one two three same as what one twenty three okay you should not consider this number as a your uh it should be a non-nonzero integer okay and therefore one two three should be assumed as should be taken as your corresponding 123.0 12 should be taken as 12.001 should be taken as 1.000 point three four six seven it has got you can see one two three four five six there are six digits we want only four digits and therefore first four one two three four and since the fifth digit is more than 5 i add 1 to the previous digit suppose if the same number is 1 12.3412 if the same number is 12.3412 you need not add one year directly you can consider 12.34 directly you can consider 12.34 therefore while taking logarithm of a particular value while taking logarithm of a particular value we should consider first four digits from the left first four digits from the left first four digit from the left in our given example we have directly taken one two three four it has got only four numbers now consider that one two three four the first two should be seen in the a segment the next one should be seen in the b segment the last one should be seen in the c segment that is very very important the first two should be seen in the a segment the next one third digit should be seen in the b segment the fourth one the last one the last digit should be seen in the c segment now before that before that this value will be equal to there are two parts one is characteristic the other one is mantissa log of any number has got two parts one is characteristics the other one is mantis are one is characteristic the other one is mandazor characteristic will be will be directly by looking at the number we can write the characteristic directly by looking at the number we can write the characteristic directly by looking at the number we can write the characteristic what is the characteristic here there are four integers there are four integers and therefore that number of integers minus one four integers as a you are corresponding before the decimal therefore that number of integers four minus one three will be the characteristic three will be the characteristic now for this thing what is the characteristic for this there are three digits therefore two point something the characteristic will be two characteristic will be 2 here 12 it is written as 12.00 out of that your a segment has got 12 and b segment is 0 and c segment is also 0. now this 12 how many digits 2 digits and therefore that minus one characteristic will be one point something characteristic will be one point something one point something similarly here we've got only one integer we have got only one integer that one minus one not this one the number of digits we have got 3 digits and therefore 3 minus 1 is 2 we have got 2 digits we have got 2 minus 1 is 1 we have got only one digit and therefore 1 minus 1 is 0 characteristic part will be zero point something and here it is before decimal we have got two integers two integer and therefore two digits and two minus one the characteristic here will be one point something one point something so i have illustrated the characteristic of this thing you may ask me a doubt sir if there is no if everything is decimal 0.1234 what is the characteristic for this definitely you may put a question and the characteristic here is there is no integer here before the decimal and therefore no integer means zero into zero minus one it is called as bar one it is called as bar one it is called as bar one it is called as bar one okay and suppose we have zero point zero one two three four then then it is called bar two because after decimal we have got one zero after decimal we have got one zero again subtract one and then therefore it is minus 1 minus 1 that is what bar 2 and suppose if we have got point 0 0 1 2 3 4 0 0 1 2 3 4 then it will be bar 3 because 2 0's again subtract one bar three therefore characteristic will be like this for the those numbers which do not have the integral part which do not have the part before the decimal if the number does not have any any particular digit before the decimal then the characteristic should be written like this characteristic should be written like this whereas the numbers having certain digits before the decimal the characteristic should be written like this now what about the mantissa for man these are alone we have to see the corresponding table format is alone we have to see the corresponding table format is all alone you have to see the corresponding table now what about 1 2 3 4 12 12 should be seen in the a column you can see just 12 under 12 the next in b segment 3 the number 3 is there so therefore under 12 go to the column having 3 in the b segment under 12 go to the column having three in the b segment under 12 go to the column having three in the b segment the number the number which is the intersection point is what point zero eight nine nine in this table it is point zero eight nine and therefore point zero eight nine nine point zero sorry eight nine nine okay zero eight nine it's not point zero eight nine nine don't say point okay twelve under three it is 0 8 9 9 0 8 9 9 now under c in the same column 12 in the same column 12 see the value under 4 in mean difference in the same column 12 c the value under 4 in mean difference in the same column 12 see the value under 4 in mean difference it is 14 add here 14 0 8 9 9 plus 14 we are going to have 3 1 10 11 1 and again which is nothing but nine so therefore zero nine one three don't neglect the zero don't neglect the zero don't neglect the zero the answer is three point zero nine one three the answer is three point zero nine one three characteristic is taken from the four digits and mantissa is taken from the table value how to take the table value children from the a segment from the a segment have the reference as a column a segment gives the reference column a segment gives a reference column a segment gives a reference column so the reference column should have 12 now 12 under that particular sorry row array in a segment a segment a segment is in the column and that row should be chosen a segment is in the column and that is the first column and that row should be chosen wherein 12 is there 12 and therefore under 12 choose the corresponding row choose the corresponding row and then in b segment three is there and therefore drop your moment from three and these two will intersect at the point that that value is point zero eight nine nine twelve and three twelve in a segment 3 in b segment will intersect at 0.0899 12 in a segment under 3 in b segment this is 12 in a segment in a segment and 3 in b segment they will intersect to give the value 0 8 9 9 and then in the same row in the same row see the value of the corresponding see the value present under 4 in the c segment see the value in the same row see the value present under 4 in the c segment that is 14. you can check there children it is 14 yeah 14. and therefore add that 14 here you will get 0.0913 3.0913 is the corresponding log value therefore log of 1 2 3 4 will be equal to 3.0913 log of 3.010913 sorry log of 1 2 3 4 will be equal to 3.0913 now what about log of your 123.4 the same mantissa will come why the digits are same and therefore same mantissa is going to come 0.0913 but what about the characteristic value there are three digits and therefore two point something two point something two point zero nine one three now what about log of twelve point three four same four digit therefore mantissa will not change zero nine one three what about the characteristic two digit and therefore two minus one is one logarithm of one point two three four same amount is a point zero nine one three we have got only one digit and therefore it is what one minus one is zero zero point zero nine one three now we are going to have log of zero point one two three four and again you can see you can see the first non-zero digit the the first in the four digits from the left but the first resist should not be zero you can see the first four digits from the left but the first digit should not be zero but the first digit should not be zero you cannot say zero one two three no it is not zero and three there is no entry in the a segment under log table under log table you can see there is no entry in the a segment which starts with 0 no it starts with 10 and therefore you cannot understand this as 0 1 2 3 you have to take as 1 2 3 4 this 0 should not be considered since there is no integral part since there is no digit here 0 digit minus 1 we have bar 1.0913 bar 1.0913 in a similar manner logarithm of your corresponding 0.01234 will be equal to there is there is zero after decimal only one zero before the decimal that is before the decimal if there is no integer part then this bar one after the decimal we have got one zero immediately after the decimal therefore it should be bar two like this like this should be about two point zero nine one three bar two point zero nine one three about two point zero nine one three therefore i hope now we have understood how to take logarithm logarithm of a given number should be written in terms of two particular parts one is characteristic the other one is mantissa one is characteristic the other one is mantissa characteristic you know spelling mandates m-a-n-t-i-s-s-a the characteristic part depends upon the number of integers before the decimal characteristic part depends upon the number of integers before the decimal mantis mantissa depends upon the four digits the four digits from the left and the first digit should be non-zero first digit should be non-zero out of the four digit definitely the first two digit should be should be considered in the a segment should be considered in the air segment the third digit should be considered the b segment the fourth digit should be considered in the main difference that is in the c segment that is main difference and how after locating the corresponding segment then you have to see the values in the entries in the values or the entries in the table now is here 12 in the a segment so mark 12 there and then 3 in the b segment so mark 3 there and then make your three column down bring this 12 row big the bring the row row you can you can even keep a scale or a pencil and then mark the corresponding intersection point 12 12 the the row which has 12 in the a segment and the corresponding three the the b segment the entry is 0.0899 and add the corresponding the same row the entry across entry along your 4 along 4 in the c segment and that is 14 that is 14 add that you will get the corresponding mind is ah and that's about the idea of choosing logarithm of a specific number yeah yeah i'll i'll just because now uh we uploaded the log and antelope table in the notes cell okay yeah as students wants little bit of introduction to logarithm that where and why do you use it yeah of course no doubt about it now uh the logarithm introduction where do we use it in the case of this table for this logarithm and antilog table it is used for much much only calculation there is no doubt about it without using the calculator you can get maximum of almost four decimal accuracy that is one of the idea and there is in mathematics you will study there are so many functions there there are so many functions what do you mean by function mapping one variable to another variable mapping one variable to another variable is called as function for example if i say one and i square it one square if i say 2 and i square it 2 square 3 3 square 4 4 square x x square therefore y is equal to x square is a function y is equal to x square is a function y equal to x square you put x equal to 1 2 3 4 y equal to x square is a function we generally say y equal to x square this is your corresponding square function or we can say y is equal to f of x it is called function of x it is called function of x in this particular equation your x is called as independent variable x does not depend on y x is called as x is called as independent variable y is called as dependent variable x is called as independent variable y is called as dependent variable now when you plot your x and y values in the horizontal and vertical axis we always say your corresponding this is your x axis and these are y axis actually speaking this should be called as your independent variable axis our horizontal axis is called as independent variable axis vertical axis is called as dependent variable axis vertical is called as dependent variable axis horizontal is called as independent variable axis now therefore when you plot the corresponding values you are going to get a curve and that curve depicts the nature of the graph obtained for this function y is a function of x now in a similar manner we have got this is algebraic function x square y equal to x square is an algebraic function y is equal to x cube is a cubical algebraic function in a similar manner we can have any polynomial now in a similar manner like algebraic function you have got your corresponding trigonometric function y is equal to sine x y is equal to cos x y is equal to tan x those corresponds to trigonometric function we have got not only your algebra not only trigonometry any particular shape k in general can be expressed in the form of what a curve in the form of an equation for example x square plus y square x square plus y square equal to a square this is the equation of a circle the equation of a circle x square plus y square equal to a square is an equation of a circle with your x comma y being any point on the circle and a is a radius of circle not only that center is origin x square plus y square equal to a square center is of the origin and x comma y is any point on the corresponding circle any point on the corresponding circle here center is origin the radius of the circle is a units so even this can be understood as a function y as a function of x therefore you just rearrange y will be equal to root of a square minus x square y will be equal to root of y square is s comma x square y is equal to root of s comma x square now i have just illustrated the idea of your a function y as a function of x y as a function of x in a similar manner in a similar manner y can be your any type of function of x it can be even any type of function of x now in algebra we have got a specific function called logarithmic function we have a specific function called logarithmic function we have got a specific function called logarithmic function log values log values is being associated to the function called logarithmic function y is equal to log x y is equal to log x to the base 10 when i say log i have already explained to the base 10 y is equal to log x now what is the need for this particular logarithmic function that may be a question from your point your y is equal to f of x now i say y will be equal to log x to the base 10 y will be equal to log x to the base 10 this is logarithmic function this is your corresponding logarithmic function now you may ask me why do we need such a function what is the need for the function yes that's absolutely fine now when x is you are 1 okay then log y is equal to log of 1 to the base 10 log of 1 to the base i will explain the value when x is 10 y is equal to log of 10 to the base 10 i'll explain the value when x is 100 y is equal to logarithm of 100 to the base 10 when x is 1000 y is equal to logarithm of 1000 to the base 10 okay and now it is very difficult to plot when x is 1 you are corresponding your 10 and then 100 then when you plot the value of yx as 1 10 100 000 the scale will be very difficult in terms of what your corresponding your x axis not only that the value suppose i say y is equal to x directly y equal to x it may be a straight line but when x varies as one ten hundred thousand it will be very difficult to plot in a graph it will be very difficult to plot in a graph in a graph you cannot because the you see the difference x is one x is ten x is hundred x is thousand so how do you take the scale the taking scale will be a problem now to reduce the difficulty we can have the corresponding logarithmic function now the logarithmic function is going to get defined as log 1 to any base log 1 to any base is always 0 because because b power 0 is 1 because b power 0 is 1 you bring this b here raise the 0 to power before anything to the power 0 is 1 from this we try to extrapolate the information of your logarithmic function b power 0 is 1 we know the value b power 0 is 1 but b not equal to 0 don't say that 0 0 is not defined 0 0 is indeterminate there are certain things called as indeterminate in mathematics which we cannot define and anything by 0 is infinity anything by 0 is infinity but 0 by 0 is not infinity 0 by 0 is indeterminate and infinity plus infinity is infinity infinity plus infinity is infinity but infinity minus infinity is not infinity infinity minus infinity is not even zero infinity minus infinity is indeterminate infinity plus infinity is infinity whereas infinity minus infinity it is indeterminate indeterminate are those particular set of your representation which can take any value from minus infinity to plus infinity your indeterminate indeterminate values that particular function or that particular ratio or that particular term can take any value from minus infinity to plus infinity and suppose if i say infinity plus infinity i said it's clearly infinity on infinity minus infinity i said it is indeterminate we cannot determine the value why this infinity itself is a relative value that infinity itself is a relative value what do you mean by relative value something which is infinity for me may not be infinity for bill gates 1 crore is infinity for me even ten thousand in infinity for me bill gates can spend ten thousand per minute per second i cannot spend ten thousand per minute and therefore let me understand that this is your ten thousand for me and this is your ten thousand billion dollars for your bill gates okay ten thousand billion dollar plus ten thousand put together it is also going to be infinity it is also going to be infinity but what about infinity minus infinity again i say it is 10 000 for me and it is 10 000 billion dollar okay billion dollar for gates and it is going to have when you subtract these two it's going to have minus infinity because this number is a huge value this number is a huge value suppose i understand that this is ten thousand for me and this is some other person for whom also your ten thousand is the infinite value for whom also the ten thousand is a infinite value what is ten thousand minus ten thousand it is zero it is zero and suppose other way i have the infinity as ten thousand the other person even one rupee is infinity for him a duggar i would say he's a beggar even 5 10 rupees infinity for him he can have a cup of coffee or tea and therefore it's a very very less value let me say 10. what is 10 000 minus 10 10 000 minus 10 is going to be 9 000 something it's a finite number it's a finite number it's a finite number therefore indeterminate can take any number between minus infinity to plus infinity indeterminate can take any number between minus infinity to plus infinity whereas infinity is nothing but a relatively larger value compared to the corresponding situation now having understood that b power 0 is 1 b power 0 is 1 in terms of logarithmic notation can be understood as log 1 when you take logarithm log 1 to the base b is 0 so therefore log of any number log of 1 to the base any number i would say x which is equal to what always 0 because x 4 0 is 1 and therefore this value becomes 0 this value becomes 0 what about the next one log of 10 to the base 10 log of 10 to the base 10 will be equal to 1 why it is 1 because this 10 will be equal to 10 power 1 10 power 1 10 power 1 is 10 10 power 1 is 10 therefore log of 10 to the base 10 is 1 so this value becomes 1 this value becomes 1 now you can see 1 and 10 1 9 time the difference is nine units it does not reduce to only one unit you are zero one zero one one unit okay and therefore scaling will be very easy in terms of what sorting the numbers really your corresponding graph what about this you are log off you are corresponding x is 100 log of 100 to the base 10 log of 100 to the base 10 log of 100 to the base 10 will be equal to what 2 because we know that 10 square 100 will be equal to 10 square hundred will be equal to 10 square therefore this value will be equal to this value will be equal to this value will be equal to what two now you can see x is hundred whereas log of that hundred has become what two and therefore now what is the difference previously the difference was one and ten it's nine you got reduced to what you are one previously the difference was ten and hundred ninety units got reduced to only one in a similar manner this will be corresponding three why because ten q will be equal to 1000 10 cubic thousand ten intense thousand therefore thousand log of thousand to the base ten will be equal to what three now the same thing you can see here the use of logarithm has reduced the quantum of value the size of the value the measure of the value use of logarithm has reduced the measure of value logarithm of bill gates assessed asset may be equal to maybe any one of the child parent asset in this group okay logarithm of bill gates asset will be equal to any one of the parents are said in this group maybe maybe i am very happy about that now considering this particular equation i can say logarithm of 1000 to the base 1000 to the base 10 will be understood as logarithm of 10 power 3 to the base 10 now here i have a formula log of x power a to the base 10 will be equal to a log of x to the base 10 log of x power a to the base 10 will be equal to a log of x to the base 10 this power will come to the front therefore it is 3 log it is nothing but 3 log 3 logarithm of 10 to the base 10 log 10 to the base 10 is 1 log 10 to the base 10 is 1 log of x to the base x is 1 log of a to the base a is 1 log of any number divided base to the base of same number is always one and therefore three multiplied by one will be equal to what three and again we use this we use this formula log of x four a to the base ten will be equal to what a log x to the base ten children the idea of logarithm in terms of application with respect to civics or chemistry or whatever matter may be the the very huge quantity can be understood of can be understood as a measurable finite quantity very huge quantity can be understood as a measurable finest final quantity in terms of the corresponding logarithm that is the basic use of that is the fundamental use of application in terms of what logarithm where of course i can do much more mathematics in that but we will go we will divert in terms of our attention with respect to what log table usage i hope you all understand correspondingly the log function and the difference between infinity and indeterminate and what is the use of log function in terms of reducing the magnitude of a physical quantity whatever may be the quantity the magnitude gets you reduced when we take the corresponding logarithm of that particular quantity i hope you all understood clearly children kindly give your feedback kindly give your i mean reply so that i can go with the next concept i will just clear the board and then go the next concept of your how to take anti logarithm how to take and elaborate okay yes sir taken the pole okay oh i hope i can proceed with because there is nothing to copy much higher in this particular frame so therefore i can go with the class yeah i'll just check the chat and then proceed with the next idea of i think we had got the mantis as point zero nine one three four your uh one two three four eighteen percent said is cleared what about the 11 percent why why the 11 percent is not clear maybe uh did you all join late or am i not audible or my video is very poor quality whatever may be if there's a technical issue please inform us we will try to rectify in our next session if there is an issue from your side in joining the class late then kindly revisit the session even if you are not able to understand if i am little fast please you can revisit the session and you will be in a position to understand all the concepts and we are here to guide you all kindly you can uh you can text mentors and mentors will help you and directly they can help you or they can contact us and they can get the information from our system of professors and then they can guide you i hope you all will agree till then i'll pass on to the next one now we are going to do the corresponding anti logarithm we have done with logarithm we are going to do with anti logarithm okay so then now we will understand how to use antilog table how to use antilog table now we have already seen logarithm of 1 2 3 4 will be equal to 3.0913 if i remember correct i'll check 12 under 3 is zero eight nine nine and then fourteen yeah zero nine one three that's correct that's correct so log of one two three four is three point zero nine one three now therefore this logarithm when it comes to other side we call as anti logarithm we call as anti logarithm what do you mean by that there is nothing but logarithm of 1 2 3 4 to the base 10 will be equal to 3.0913 and when we remove the logarithm when this 10 comes this side 3.093 will go to the power therefore 1 2 3 4 will be equal to 10 power 3.0913 10 power 3.0913 10 power 3.0913 children please understand it is 10 power 3.0913 now this is nothing but your anti loss this this thing can be expressed as 1 2 3 4 will be equal to anti logarithm three point zero nine one three so when we take anti-log of this number when we take anti-log of this number we will get definitely one two three four how to understand that very simple children now until algorithm of your 3.0913 anti-logarithm of 3.0913 now in anti-logarithm while using the table while using the table for anti-logarithm we have to use for anti-logarithm the first four numbers after decimal first four numbers after decimal first four numbers after decimal first four numbers after decimal so then you may ask me a question sir should we consider this zero yes we have to consider the zero why because antilog table starts from point zero zero antilog stable starts from point zero zero antilog table starts from point zero zero therefore we have to consider your first four numbers after decimal first four number after decimal in the anti-log table definitely here the first four number is what zero point zero nine one three don't worry about this don't worry about the characteristic take only the mantissa take only the mantissa your point zero nine one three this is your corresponding mantissa children while taking logarithm forget the characteristic now you are 0.0913 the first two should be seen in the a segment you are the third one should be seen in the b segment the last digit should be seen in the c segment the same principle the same principle there is no deviation there is no deviation in terms of looking the values in your log and anti log table only the a segment values will differ that's all now a segment point zero nine you can see under point zero nine one so under point zero nine freeze that row under point zero nine freeze that row under point zero and freeze that row and then from one b is one therefore in the b segment under one bring under one and then point zero nine row point zero in row the meeting value will be one two three three the meeting value will be one two three three therefore a is point zero nine and b is one the meeting value will be one two three three the meeting value is one two three three the meeting value is one two three three what about the corresponding you are three mean difference is three main difference three under three under three in the same row under 3 if you see you have the value 1 in the same row under 3 if you see you have the value 1 therefore c value is 1 add that 1 here 1 2 3 4 1 2 3 4 therefore anti-log of this is one two three four okay anti log of this is one two three four not only that not only that you blindly put your corresponding zeroed on that is you have all the numbers all the numbers obtained from anti-lock table as just after the decimal zero point one two three four you take point zero nine one three you take the anti logarithm have this as 0.01234 now this is the value corresponding to anti-lock table for your 0 9 1 3 not the characteristic not the characteristic not the characteristic how to use the characteristic children multiplied by 10 power c plus 1 c plus 1 y c plus 1 characteristic plus 1 previously we subtracted 1 with respect to the number of digits before the decimal in while taking logarithm while taking logarithm we subtracted we had log of logarithm of one two three four will be equal to three point zero nine one three dot that was the value how this since these three came it is four digits and therefore four integer path four minus one is three the rule i said in a similar manner there we subtracted one the integer part number of integer part or the number of digits before the decimal minus one here the same thing we have to add here that's all c plus one characteristic plus one characteristic plus one characteristic plus one therefore it is point one two three four multiplied by ten power three plus one point one two three four multiplied by c is three ten power three plus one that is equal to point one two three four multiplied by ten power four point one two three four multiple evidence for this nothing but ten thousand therefore one two three four multiplied by ten thousand is going to give you one two three four point one two three four multiplied by ten thousand is going to give you one two three four therefore anti logarithm of your corresponding three point zero nine three will be equal to what one two three four logarithm of one two three four is point three point zero nine one three and anti logarithm of three point zero nine one three will be equal to what one two three four and that's about the idea of usage of log table and antelope table i hope children kindly give your concern about the usage of log table and antilog table if you are able to understand we may do some more numbers i am going to give you some more calculation with some numbers and then finally we are going to do the problems in ph okay i hope you all agree with that yeah please take the pole map yeah yeah yeah please please because we have done with the log value on the same value as anti-log table and therefore personally i feel there should not be any great confusion in the minds of children but they can also verify the value in terms of what the corresponding okay this is only logarithm it is not multiplication or division for multi maybe they can they can verify this in calculator they can verify this 10 power 3.0913 they can verify this 10 power 3.0913 in calculator whether it comes to 1 2 3 4 or not nearly it will come nearly one two three four definitely i'm waiting uh for the reply from you all children i think i can in the meantime i can clear the board so that the time won't be wasted we can use the time more productively for doing some more calculations in terms of using logarithm and anti-logarithm and we can do problems with respect to what ph that is the core idea of this particular class doing problems with respect to ph okay and definitely i want to do some problems with respect to ph and using the principle of your logarithm and ideal algorithm we want to do that so i hope 80 percent said that it is clear again the percentage gone down i don't know why maybe for somebody some people uh they did not even answer the poll eighty-five percent said is clear now for five percent got increased that's okay no problem so kindly children if you have any specific doubt with respect to seeing the values in long and anti-lock table please inform us maybe to the mentor and if the question is very critical mentor will forward to us or else they themselves will answer your question and if the question comes here definitely i am prepared to want the answer whatever the type of question you are going to ask here okay we are very happy we will be very happy to answer all the questions what you ask for okay now coming on to the uh calculation with respect to log calculation we will do some one or two fractions uh and then with smaller fraction and then with the larger fraction and then we can go with what some more ideas of ph yeah children are asking can you repeat logs once again yeah definitely i'll repeat i'll do problems simple numbers and while doing this numbers definitely you will understand your log table usage of log table and analog table once again okay definitely log table you will understand easily okay because when you understand the log table antilog table is a similar one you can just like that understand the anti-lock table also now i am going i am not going to repeat the same thing what i had done before i am going to do some calculation now let us consider your the number 29 divided by 13 i have taken 29 by 13 maybe prime number okay how to go about calculating this let x is equal to 29 by 13 let x is equal to 29 by 13 that x is equal to 29 by 13. how to calculate the value children now i don't want to divide i want to go with logarithm take logarithm log x will be equal to log of 29 divided by 13 log x will be equal to log of 29 divided by 13 now there is the formula in logarithm log of x divided by y log of x by y to the base 10 whenever i put log to the base 10 that will be equal to log x minus log y log of x by y will be equal to log x minus log y something in division has become very easy in terms of subtraction something in division has become very easy in terms of subtraction in a similar manner log of x into y will become log of x plus log of y so something in multiplication has become very simple in terms of addition and that is also one of the wonderful application of in terms of logarithm a huge number two multiple product of two huge numbers can be understood as the sum of its corresponding logarithm the quotient of two huge numbers can be understood as the subtraction of the difference between the corresponding their log values now and i am going to apply this formula here that is going to be log of 29 minus log of 13 log of 29 minus log of 13 this is your log x okay now what is log 29 children log 29 now this log 29 should be understood as log of 29.00 because while taking logarithm i clearly told you all you should have four digits from the left should have four digits from the left first four widgets from the left first four digits from the left we have only two digit and therefore add two more digits as a decimal part add two more digits a decimal part add two more this is as a decimal part now therefore we have got 2 9 0 0 out of this this is decimal part this is integral part and therefore now log of 2 9 0 0 the first two digit should come in a segment the third one should come in b segment the last digit fourth digit should come in c segment and that segmentization the first two is a segment the next one is b segment the last one is in c segment here b segment is 0 c segment is also 0 and obviously c segment will not contain any value under 0 because there is no number as 0 will be in the c segment c segment consists of only 1 to b segment consists of your zero to nine whereas a segment consists of in logarithm 1 0 10 to 99 in terms of anti logarithm it contains 0.00 to 0.99 right now therefore log of 29 should be understood as log of 29.00 we have got four digit out of the four digit 29 should be the corresponding a part and 0 is the b segment and the c is again 0 is another entry in the c segment now we have got how many integer children two integer part two in two minus one the number of integral part before the decimal the number of this is before the decimal minus one the number of digits before the decimal minus one the number of digits before the decimal minus one is the characteristic part therefore the characteristic part is one point why it is one point two digit therefore two minus one is one one point what is the amount is the value mandatory value should be seen in the log table using this entry my mantissa value should be seen in the log table using this entry under 29 see you see that in the table 29 6 that true 29 fix that row and don't worry about your corresponding c because c does not does not have a zero entry here c does not have been mean difference there is no entry under zero and therefore that you can always neglect 29 fix that row and then b segment you should see the value under 0 29 under 0 it is 4 6 2 4 29 under 0 it is 4 6 2 4 29 under 0 is 4 6 2 4 therefore the value is one 1.4624 four six two four logarithm of 29 is one point four six two four one value we have found what about the next one log of your thirteen logarithm of thirteen will be equal to again i am going to write as logarithm of thirteen point zero zero again thirteen zero zero this will be see this should be seen in the a segment this is the b segment and this is in the c segment now that is equal to again two digit again two digit before the decimal two digit before the decimal two minus one is one two minus one is one this one is nothing but number of digit minus one this one is nothing but number of digit minus one now under third in a segment under 13 13 fix that row and then under 0 under 13 fix the draw under 0 1 1 3 9 and c segment 0 will not come don't bother about that and therefore under 13 under 0 it is 1 1 3 9 1 1 three nine one point one one three nine yeah correct one point one one three nine now substitute this value here children you are one point four six two four minus one point one one three nine i am going to subtract here 1.4624 sorry 1.4624 and then minus 1.1139 you can see the numerator is higher than denominator the numerator is higher than denominator this value will not be negative the numerator is higher than denominator this value will not be negative the numerator higher than denominator this value will not be negative and always while taking logarithm you have to adjust the numerator in terms of your higher value than the denominator that is one particular simple a logical method i will explain later okay now this is you borrow 1 here 14 minus 9 is 5 and then 11 11 minus 3 is 8 and then 5 5 minus 1 is 4 and then 4 minus 1 will be corresponding three zero point three four eight five zero point three four eight one point four six two four divided by sorry minus one point one one three nine will give you point three four eight five i hope my subtraction is clear 14 minus 9 is 5 and then 11 minus 3 is 8 and then 5 minus 1 is 4 4 minus 1 is 3 correct now therefore it is nothing but log of x will be equal to 0.3485 log of x will be equal to 0.3485 now we have found log x we have not found x we want x x is 29 by 13 we want x we have found only log x therefore now let us find your corresponding x by taking anti logarithm of the right side value log x will be 0.3485 log x will be 0.3485 what is x anti logarithm of 0.3485 anti logarithm of 0.3485 while taking anti logarithm we have to consider 0.3485 alone we have to consider the decimal part alone we have to consider the decimal part alone 3 4 should be under a segment a should be under b segment and 5 should be under c segment 5 should be under c segment okay now what about 0.34 in and this would be seen in anti lock table not in lock table okay and you'll have 0.34 under sixth row point three four eight point three four under eight we have got two two two eight point three four under eight you have got point three four eight five point three four under eight you got two 2 2 8 and therefore 2 2 2 8 okay and then under 5 under 5 you have got 2 2 to 8 under 5 you got 3 under 5 over 3 under 5 you have got 3 added 3 here there would be 2 2 3 1 2 2 3 1 2 2 3 1 now i clearly told you keep keep your point 2 to 3 1 as a value point 2 2 3 1 multiplied by multiplied by 10 power 0 plus 1 this is your characteristic value 0 plus 1 because while taking logarithm while taking logarithm we subtracted the number of bases by 1 we subtract the number of resist by one we subtract the number of digits by one to find the characteristic part two digit minus one is one similarly two digit two digit minus one is one so while taking logarithm to find the characteristic part we subtracted one from the number of digits while taking anti-logarithm while taking anti-logarithm 10 power that characteristic plus one we have to add plus one that is zero plus one is one zero plus one one is zero plus one is one ten power 1 is 10 therefore this becomes 2.231 the x becomes 2.231 x is nothing but 2.231 now therefore 29 by 13 will be equal to 2.231 29 by 13 will be equal to 2.231 now we can check with the calculator children you can also check i am also going to check here you are 29 divided by 29 divided by 13 29 by 13 will be equal to two point two three zero seven the answer is from the your uh calculator from the calculator i'm getting the value as two point two three zero seven six two point two three zero seven six you can see the accuracy two point two point two three zero seven six is the calculator value zero seven six nine is the calculator value our value is two point two three one you see the up to third decimal accuracy we are almost correct we are almost correct and therefore the ratio 29 by 13 is 2.231 it is not necessary that we should use calculator we can also use log table if you practice the corresponding usage of log and antilog table definitely the calculations will be very very easier i hope you all follow children clearly kindly let me know madam you can just uh again you can ask them or some people can reply if you are able to follow yeah yeah thank you madam so i'll wait for one or two minutes so that if somebody they have not taken the notes they can also copy i i let me not quickly rub the entire information from the board because i want all the children to understand the concept pretty well if i am fast please tell me i will reduce my pace if you want to repeat please tell me because why i did not repeat the previous one because the same rule i am giving here how to take logarithm i have given here how to take logarithm i have given here how to take anti logarithm i have given here therefore while doing calculation if you practice more such calculation definitely log and analog will be very very easy for you all it will be highly useful in terms of your practical exam in 11th or 12th not only that in terms of understanding certain physical chemistry problems with respect to what either j main or need but definitely you will be given options with respect to what your question and when the options are there a log table they won't give and you have to go by number mathematics but in cvsa exam definitely you need to know the log values for certain thing that is very very important not only that in certain physical chemistry lessons you will have the log function three into log of a by t into log of a by a minus x that formula will come in chemical kinetics in next year and not only that you have got so many other functions uh also uh involved logarithmic equations also involved in chemistry not in chemistry but in physics also i hope you all understand clearly children i'll go to the next one yeah i am going to give you one more calculation involving some other numbers with denominator more than the numerator okay denominator more than the new here numerator is more than denominator now i am going to give you one more uh calculation we are going to do both on the board one more calculation wherein the numerator is lesser than the denominator or the denominator is higher than the numerator when the denominator is higher than the numerator we are going to end up with fractions and directly i am not going to teach you how to take your bar i already told you when there is no integer part before the decimal then you should have bar 1 bar 2 bar 3 etc but i am not going to teach you why that rebar representation because i feel personally bar is a unit of pressure bar is a unit of pressure bar is a unit of pressure when i say bar pressure you will get more pressure and therefore we will not go by that method i will illustrate this some numbers and then we will uh discuss uh 14.3 divided by your corresponding uh 390.7 i just noted from some of the calculation in 12 standard so the next is x will be equal to 14.3 divided by 390.71 14.3 divided by 390.71 14.3 divided by 390.71 now when you look at this equation or this fraction you can see the numerator is much lesser than the denominator numerator is much lesser than the denominator when the numerator is much lesser than the denominator please do not take logarithm as such please do not take logarithm as such please do not take logarithm as such y sir because log of numerator log of numerator minus log of denominator will be negative why because log of the numerator is less than denominator then log of numerator will be less than log of denominator then you will end up with a negative value this negative value while taking anti-logarithm it while taking anti-logarithm of a negative value we will have lot of confusions we will have lot of conclusions not only that not only that even even in this calculation also suppose i am going to have a number like this 14.3 divided by your 0.390 then keeping this number as such is also not advisable keeping this number as such is also not addressable because while taking logarithm while taking logarithm please ensure that you have got some decimal part at least one integral part at least one integral part at least one integral part at least one integral part this is very very important concept children for ease of calculation at least one integral part should be there why because that integer part minus 1 will give you what the corresponding because there is only one integer 1 minus 1 is 0 and therefore you will take you will have the log value as zero point something you will not have bar one you will not have borrow two you will not have bought three suppose if i am if i am going to have zero point one two three four i am going to consider this as if i directly take logarithm i will have bar 1 but when i consider this as 1.234 multiplied by 10 power minus 1 1.234 multiplied by 10 power minus 1 i'm going to use only this for log calculation not for not not this then then your calculation will be very very easy then your calculation will be very very easy now i am going to consider here please see children now x will be equal to 14.3 divided by 390 390.71 okay i'm not going to take this equation directly numerator as log of log x and then the corresponding log of 14.3 minus log of 390.71 i am not going to do i am going to use the principle of numerator more than the denominator i am going to adjust the equation numerator more than the denominator how to adjust the equation children this is 14.3 divided by this can be understood nine as seven one multiplied by ten square this can be understood as three point nine zero seven one multiplied by ten square three point nine zero seven one multiplied by ten square fourteen point three i'm not going to alter that fourteen point three divided by 3.9071 multiplied by 10 square i am going to move this 10 square to numerator therefore x will be equal to 14.3 divided by 3.9071 multiplied by 10 power minus 2 now you see the ratio now i have got the ratio wherein the numerator is more than the denominator now i have got the ratio where the numerator is more than the denominator therefore i am going to consider y is equal to 14.3 divided by 3.9071 14.3 divided by 3.9071 now what is log y children log y will be equal to your 4 log of 14.3 log of 14.3 log of 14.3 minus logarithm of 3.9071 now what is logarithm of 14.3 children i can understand 14.3 as what 14.30 and therefore this will be your a path and this is your b part and this is your c segment okay the number is the c segment what is 14 under 14 under 14 under 3 under 14 under 3 1 5 5 3 1 5 5 3 therefore two digits there there are two digits therefore it should be one point two digit two minus one is one one point it is one five five three and then your mean difference is zero there so therefore the c segment no value directly only a and b segment intersection value we can take 14 under three point five one five five three therefore one point one five five three one point one five five three one point one five five three that is your log of fourteen point three what about the next one children log of three point nine zero seven one log of three point nine zero seven one this is nothing but how to under how to take the value children the first left 39 should be under a segment 0 under b segment and 7 should be the c segment i need not add one here because the next digit is only one the next digit is only one suppose if the next digit is five or more than five three point nine zero seven five three point nine zero seven six three point nine zero seven seven three point nine zero seven eight three point nine zero seven nine then then if this is more than five or equal to five then this number seven can be arranged as eight or can be rearranged as 8 can be reformed as 8 but no it is not necessary because that is 1 and therefore neglected 3 under 39 under 39 the row value is 39 under 39 under 0 39 under 0 is what you are 5 9 1 1 ok under 7 you can just take the value 7 children under 7 it is 8 under 7 it is 8 under 7 it is 8 therefore 5 9 1 1 8 i'll just check once again children under 39 under 0 it is 5 9 1 1 39 under 0 is 5 9 1 1 under 7 it is what under 7 it is 8 ok this is nothing but 5 9 1 five nine one nine now we have got only one integer part we have got only one integer part we have got only one integer part therefore it is zero point one minus one is zero zero point five nine one nine zero point five nine one nine zero point five nine one and therefore log of fourteen point three we have calculated log of three point nine zero seven one we have calculated now we have to subtract these two subtract these two you are one point one five five three minus zero 0.5919 now when i subtract i am going to end up with a positive value i will not have a negative value y should not be have a negative value ending with the negative value in terms of anti logarithm will have some confusion not only that why do we arrange like this why not 39.01 0 7 if it is 39.00 our numerator will be less than again denominator if it is 0.3907 yeah you can arrange this 0.3907 but you will end up with bar one you will end up with bar one bar is a unit of pressure bar is a unit of pressure and therefore i will not recommend my children to be stressed or to be with pressure and therefore go don't go with bar calculation please free of birth when you when you are free of bar you are free of stress and pressure and therefore now you can easily subtract 13 minus 9 which is nothing but 4 and then 4 minus your 4 minus 1 is 3 and then 15 minus 9 is 6 and then you just 10 minus 5 is 5 okay and therefore it is 0.5634 0.5634 now what are the value children you are i i said 0.5634 is nothing but the subtraction value log of this value log of y log of y will be equal to 0.5634 i hope my calculation is correct 13 minus 9 is 4 4 minus 1 is 3 and then input here 15 minus 9 is 6 0 and then 10 minus 5 is 5.5634 correct and therefore this value is 0.5634 therefore log y will be equal to 0.5634 what is y children anti-logarithm point five six three four anti logarithm of point five six three four under this your first two should be seen under a segment three b segment four c segment that should that is that is under anti-lock table okay five six six the five six as row therefore point five six it is rho is point five six and then under three we have to see under three under three it is three six five six three six five six three six five six and then four under four the value is three the value is three three six five nine three six five nine zero point three six five nine multiplied by ten power zero plus one ten power zero plus one ten power zero plus one zero plus one one therefore three point six five nine y value is three point six five nine you can logically calculate you've got 14.3 by 3.9 14.3 by 3.9 14.3 by 4 approximately 4 it is more than 3 you can see that it is more than 3 oh yeah the nearly nearly the correct value we are approaching so why we have found what is y children what is x children x is y multiplied by 10 minus 2 x is y multiplied by 10 minus 2 x is y multiplied by n power minus so therefore x will be equal to 3.659 multiplied by 10 power minus 2 therefore x will be equal to 0.03659 x will be equal to 0.03659 14.3 divided by 390.71 will be equal to 0.03659 and i am going to check with the calculator children i am going to check with the calculator 14.3 minus 14.3 minus uh sorry not minus divided by divided by 14.3 divided by your 390.71 390.71 will be equal to 0.0366 the calculator value x calculator will be equal to 0.0366 okay that is the value you can see the accuracy 0.03659 and 0.0366 you see the accuracy children it almost matches 0.03659 and 0.0366 it almost matches therefore the use of logarithm and anti-logarithm in terms of doing the calculation of such ratios and fractions will be very very useful in terms of your application children are you all clear kindly kindly uh please text me or madam you can maybe make a poll so that after that i will clear i don't want to clear immediately because i want children to copy if somebody has not copied then i want to i have taken the polls thank you madam thank you very nice of you madam so oh i think it's now time for us to go with ph calculation we will go with ph calculation because it's already 6 uh 18 so now we have introduced how to use log and anti-lock table and now i am going to discuss how to use the same in terms of what your corresponding ph calculation okay so after getting there is a pole result yeah 98 percent said concept is clear thank you children hats off to you hats off to you it it means that all of you are listening the class very carefully all of you are listening the class very carefully it is not because of lakshmana handling the class you are able to understand no it is because of pure your concentration you are able to understand the class then that's a very great attitude of all children i am very proud of you god bless you all with more and more concentration focus to clear your jee or neet or kvpa or whatever the company examination you're going to appear after your 12th standard with a very very very high score for the same reason only we used to pray we used to pray during the beginning of any class we have the we are the habit of praying for the children because i feel personally prayers are the only ray of pope in life prayers are the only ray of hope or in life that is i personally feel and i've also experienced that in my life and hence i always wish to pray pray pray pray then definitely the ray of hope will come in life no doubt about it it is going to come okay it may be some some people will will say it may be in the form of god or in the form of somebody no no problem let it come in the form of human being or anything but it is a hope in life that is very very important now we are going to apply this concept in terms of ph calculation okay now children what is ph ph is nothing but power of hydrogen ion or power of hydrogen concentration power of hydrogen concentration it is also called as hydrogen potency it is also called as hydrogen potency or hydrogen ion potency hydrogen ion potency now ph is mathematically defined as negative logarithm of hydrogen ion concentration when we put square bracket like this it is called concentration we also refer this square bracket as active mass active mass active mass active mass is that mass of the substance or that substance which takes part in the reaction actively that is called active mass and ph is defined as negative logarithm of hydrogen ion concentration this is hydrogen ion negative logarithm of hydrogen ion concentration ph is defined as negative logarithm of hydrogen ion concentration similarly we can define pys similarly we can define pois negative logarithm of hydroxyl ion hydroxide ion or hydroxyl ion concentration poh is hydroxyl ion concentration for water for water ph is equal to 7 for water when the system is neutral ph is 7 and poh is also equal to 7 ph is 7 p volts is also 7 not only for water for any substance for all medium for all medium i can say ph plus medium are solutions okay for all medium or solution containing h plus and h minus ion ph plus ph is always equal to 14 ph plus ph poh is always equal to 14 ph plus ph is always equal to 14. ph is 7 for water p volt is also 7 for water some of these 2 will be equal to 14 when the ph is 5 poh will be equal to what 9 when the ph is 1 ph will be equal to 13 when the ph is 13 poh will be equal to 1 when the poh is 10 ph will be equal to 4 and you can always understand but the definition of ph is negative logarithm of hydrogen ion concentration now we are going to find the ph of 2 multiplied by 10 power minus 3 molarity find the ph of 2 multiplied by 10 power minus 3 molarity your corresponding hcl find the ph of 2 multiplied by 10 power minus 3 molarity corresponding hcl hydrochloric acid how to go about the problem children hydrochloric acid in aqueous solution that is with water it is going to give you h plus and cl minus h plus will not be remaining as x plus h plus in aqueous medium it will react with water to form corresponding hydronium ion hydronium ion so therefore put together we can write hcl plus your water is going to give you that is aqueous medium is going to give you h3o plus ion plus your chloride ion s3o plus ion that is called hydronium ion this h3o plus is called as hydronium ion and three voc is called as hydronium ion plus your corresponding cl minus okay now this is the exact equation what we should write because h plus is not stable h plus always gets associated with the medium here the medium is water it reacts with medium to form corresponding h3o plus ion that is called hydronium ion so instead of h plus we can even write it as in some other textbook you may see negative logarithm of h3o plus ion negative logarithm of h3o plus ion in some other textbook you might see a negative logarithm of h3o plus ion both are correct children if you write x plus for understanding in terms of principle you can write but in chemical reaction h plus will not form independently because it is unstable now hcl plus water gives a 3 o plus plus a minus for 1 mole of hcl we get one mole of corresponding your aco plus ion therefore for so much of molarity the corresponding concentration of hcl will be equal to concentration of h plus that is also equal to concentration of cl minus therefore concentration of h plus will be equal to the same as concentration hcl this is the concentration of hcl 2 multiplied by 10 power minus 3 2 multiplied by 10 power minus 3 molarity here the concentration of h plus is same as concentration of hcl suppose if you are given h to the 4 sulfuric acid 2 multiplied by 10 minus 3 sulfur molar sulfuric acid then sulfuric acid for each mole 2 sulfuric acid will be laboratory for each mole two exponents will be labeled for one mole of sulfuric acid one h two is a four two h plus and two s over sorry two x plus and s support two minus will be liberated maybe we can write the equation your h2 so4 will give you in aqueous medium 2x plus plus so4 2 minus if this concentration is x then here the concentration will be 2x there the concentration will be 2x in sulfuric acid the concentration is two times the concentration of water in the concentration of x plus is two times the concentration of sulfuric acid in in the case of ionization of sulfuric acid suppose if there is complete ionization of phosphoric acid phosphoric acid h3po4 complete i understand that it gets completely ionized it gets completely ionized it gets completely ionized in aqueous medium it is going to give you 3h plus and then p o four three minus p o four three minus now what is this you are if this is going to be x this is going to be concentration three x and therefore the based on the nature of the acid the concentration of x plus will vary based on the nature of the acid the concentration of x plus will vary now in this case the concentration of acid is same as concentration of x plus the same as concentration of cl minus we don't want cl minus concentration because ph depends on only h plus and therefore directly we can say h plus will be equal to r 2 multiplied by 10 minus 3 molarity now this is the concentration of h plus we know the formula ph is equal to negative logarithm h plus concentration therefore ph will be equal to negative logarithm of what is the concentration of h plus children it is 2 multiplied by 10 power minus 3 2 multiplied by 10 power minus 3 now that is equal to minus log of x into y it is log x la plus log y okay when log of x into y all of x into y is log x plus log y already we have we have given the formula children this is log x plus log y now i'm going to multiply this minus n inside minus log 2 this minus into plus will become minus log of 10 power minus 3 log of 10 power minus 3 what is the value children log of 10 power minus 3 will be equal to minus 3 into log of 10 to the base 10 because when i say log it is to the base 10 and this minus 3 will come already we have given the formula log of x 4 a is a log x log of x 4 is a log x log of x 4 a is a log x we have already given the formula in a similar manner that minus 3 will come to the front and log 10 to the base 10 is 1 and therefore that is equal to minus 3 into 1 will be equal to what minus 3 minus 3 into 1 will be equal to -3 this value is minus 3 this value is minus 3 minus into minus 3 will become plus 3 therefore minus log 2 plus 3 or i can see 3 minus log 2 3 minus log 2 log 2 when you see in the table log 2 when you see in the table you have to see under 20. 2 means 2 means it is 2.000 it means the first 2 digits should be in the a segment 20 the third is your b segment zero mean difference is zero and therefore c segment value is also zero z c segment we need not worry because zero is not there so therefore under twenty under zero when you see the value will be point three zero one zero when you see under twenty it is three zero one zero okay and therefore we have got two log two only one integer only one integer therefore one minus one is zero and therefore that is equal to three minus point three zero one zero three minus point three zero one zero three can be understood as three point zero zero zero three point zero zero zero zero and point three zero one zero and don't worry about the last zero your ten minus corresponding your one will be 9 9 minus 0 is 9 and 9 minus 3 will be equal to 6 and 2.669 2.66 and therefore the ph value will be point 2.699 nine nine the ph value will be two point six nine and therefore the ph of two multiplied by ten power minus three molar concentration hcl is two point six nine nine obviously for azure system ph will be less than 7 for basic system ph will be more than 7 for neutral system ph will be equal to 7. here it is azurite system because it is hydrochloric acid and therefore is ph is less than 7 which is and of course the concentration is not that much lower value it's a very good value two multiplied by n minus three is a very good value because when i say ph is seven what is what does this imply ph is seven implies that the concentration of h plus will be equal to 10 power minus 7 molar concentration of x plus will be equal to 10 power minus 7 molar concentration of h plus concentration of h plus will be equal to 10 power minus 7 molar then only the ph will be equal to what negative log of x plus negative log of 10 power minus 7 negative log of 10 power minus 7 negative log of 10 power minus 7 minus 1 will come here minus of minus plus 7 into log of 10 to the base 10 7 log of 10 to the base 10 is 1 log of 10 to the base 10 is 1 7 into 1 is 7 therefore ph will be 7 ph will be 7 when ph is 7 the concentration of h plus is 10 power minus 7 molar 10 power minus 7 is much much lesser than what 10 power minus 3 10 power minus 7 is much much less than 10 power minus 3 or 10 power minus 3 is much much higher and therefore and therefore your ph will be much lesser than your 7 and we got the value as 2.699 and then we are in the right direction with respect to the ph calculation and that's about the idea of your calculating or your ph using the logarithmic principle for a particular hazard system yeah children kindly please madam you can initiate a poll and then you can tell me if everything is fine i'll go with the one more problem taking the pulsar thank you madam thank you very good i hope mentors are doing a great job with all your permission of the mentors as well as the organizers and your children i will have a small sip of water because i have some little problem yeah we are going to do one more problem in the same test similar type i am going to do one more problem of the similar type with respect to what your ph calculation but with some some more intricate concept okay that is what i i am going to do in the next one previously i just i got mislead okay okay sorry madam sorry extremely sorry thank you children i hope all the children are doing a great job and they are listening the class very carefully taking the notes also and that is the reason why we get so much of uh good percentage of children they are able to understand because their attentiveness in the class is good and that is a primary requirement for any child to have a better knowledge transfer knowledge transfer will come only when the child cooperates to the maximum extent and of course there is a role of treats and no doubt about it but but when the cooperation of child is from self from within then the efficiency of knowledge transfer is maximum its maximum we call as there is a principle called induction and we have got self induction and mutual induction in in physics you might have studied in electricity electromagnetic induction there are two types of electromagnetic induction one is self induction the one is mutual induction and self-induction is inducing ourselves with the from within that is very very important and mutual induction mutual induction is getting induced from outside from external source like your newton saying that all forces are external and that is your mutual induction whereas our indian rich culture says that everything is from internal everything is from internal our indian culture says that everything evolves from within and don't worry about children let me not talk too much of philosophy i'll go with the next one okay now i am going to do one more problem with some different value of what your corresponding hcl concentration find the ph of 10 power minus 8 molar hcl 10 power minus 8 molar hcl again hcl plus water is going to give you h3o plus ion plus cl minus okay now the concentration of your this is x and this is also x and that is from your acid alone okay that is from acid alone or the value of h plus concentration of hcl will be equal to concentration of h plus this is from acid okay from acid that is equal to what 10 power minus 8 molar d suppose if you are using this value for the ph what are the ph children ph is negative logarithmic hydrogen ion concentration that is equal to minus log of 10 power minus 8 minus 8 will come to the front therefore minus of minus 8 multiplied by log 10 when i say log 10 it is the base 10 this value is 1 and therefore minus of minus 8 is plus 8 into 1 will be equal to 8 and therefore ph will be equal to 8 and hence your ph of 10 power minus eight model at sale is eight this is wrong why because for azure system we know that your ph is seven it is neutral less than seven to zero okay seven to zero okay less than 7 it is azerite system 7 to 14 it is basic system and this is your ph scale okay therefore whenever we say hcl is a hydrochloric acid how come hydrochloric acid system or other system can have a ph 8 ph 8 is the basic value ph 8 is the basic value ph cannot be had ph can never be a for a basic system sorry for an azerite system ph can never be a for another system because for another system ph should be less than seven it is less than seven it is less than seven then you may ask me you might tell me sir it's a very very low values are 10 power minus eight molar is a very low values are even when it is much lower it should be very close to 7 it cannot be more than 7 it cannot be more than 7 ph of another system can never be more than 7 ph of an azerite system can never be more than 7 ph of another system can never be more than someone and therefore this calculation is wrong now in such cases the concentration of h plus should be equal to concentration of x plus from acid plus constant region of x plus from water because always concentration of h plus from water is equal to 10 power minus 7 molarity always concentration of h plus from water it is 10 power minus 7 molarity always concentration of h plus from water is 10 power minus 7 molarity you see 10 power minus 7 is more than 10 power minus 8 10 power minus 7 is more than 10 power minus 8 10 minus 8 is less value and therefore we have to sum both the concentration we have to add both the concentration now therefore the net concentration of expression will be equal to what is the concentration of expression from acid the concentration of exponents from acid is what 10 power minus 8 plus the concentration x plus from water is 10 power minus 7 we have to add both the concentration to get the total concentration of x plus and so much of molarity now i can make this as 10 power minus 7 multiplied by 10 power minus 1 a power m into a boron is equal to a 4 m plus 1 multiplied by 10 power minus 7 okay and i can take 10 power minus 7 sorry plus 10 power minus 7 i can take 10 minus 7 common when i take 10 minus 7 common it is 10 power minus 7 1 by 10 is 0.1 this is 10 power minus 1 is 0.1 1 by 10 0.1 i have taken 10 power minus 7 outside therefore it's become 1 therefore 1 plus 0.1 is 1.1 multiplied by 10 power minus 7 1 plus 1 is 1.1 multiplied by 10 power minus 7 therefore therefore concentration of x plus is your 1.1 multiplied by 10 by minus 7 molarity concentration of x plus total will be 1.1 multiplied by 10 minus 7 molar then you may ask me a question sir in the previous problem you did not add the concentration of x plus from water side why is that it was 10 power minus 3 and 10 power minus 7 10 power minus 3 and 10 power minus ten thousand times what lesser and therefore it's going to be affect only you're going to get affected only the fourth decimal or the fifth third is going to get affected don't bother about that it is much much much much you are farther away and therefore we have neglected when you add 10 power minus 3 and 10 power minus 7 it is you can see it's meaningless because it is the second term is much much much much lower and therefore we did not consider for too much azerite system we did not consider 10 power minus 7 molar h plus from water but for a very dilute system for a very dilute system for a very dilute system definitely for dilute acids and dilute bases you have to consider the concentration of x plus from water the concentration of y x minus from water for a base calculation okay right for a calculation regarding y minus now constant is 1.1 multiplied by 10 minus 7 molar therefore what is ph ph will be equal to negative logarithmic concentration of h plus or negative logarithmic why is an ion concentration ph will be equal to negative logarithm what is x plus concentration children 1.1 multiplied by 10 power minus 7 1.1 multiplied by 10 power minus 7 that is equal to minus of log of 1.1 plus log of 10 power 7 minus 7 10 power minus 7 this minus 7 will will come to the front and therefore i am going to multiply this minus log of 1.1 minus of minus 7 multiplied by log 10 to the best and this value is 1 therefore minus log of one point one minus n minus plus seven seven into one is seven that is equal to seven minus log of one point one therefore p h will be equal to seven minus log of one point one now we have to see the value of log of 1.1 how to see children log of 1.1 can be understood as log of 1.100 1.100 this 2 11 should be the a segment and 0 should be the b segment and c of course c 0 in c segment 0 it's meaningless you can not worry therefore what about log 11 log 11 will be 0 4 1 4 it is 0 4 1 4 0 4 four therefore we have got only one integer part we have got only one integer part therefore zero point zero four one four zero point zero four one four i'll again check the value children for one of clarity eleven zero four one four correct therefore this is equal to 7 minus 0.0414 now we have to subtract 7 is 7.000 0.0414 10 minus 4 is 6 9 minus 1 is 8 9 minus 4 it is say you are corresponding 5 and then you are 9 and then 6 6.9586 therefore it is 6.95 eight six you can see the ph is very close to seven but not seven it is slightly less than seven but it's azerik medium y because it's at cl hcl is the other medium therefore ph should be less than seven here is hazardous medium therefore ph should be less than seven hcl is acidic medium therefore ph should be less than some we have got a value of ph of 6.9586 which is less than seven unlike the value of ph equal to eight where we have used only acid value the h plus from acid here we have used express from both acid as far as water in most of the cases wherein very dilute solutions are used in most of the cases wherein very dilute solutions are used if the concentration of the acid or base is very very less if it is a very dilute solution whether it is solution or basic selection keep in mind water will contribute for both h plus and o h minus water will contribute for both h plus and y h minus water will contribute for both x plus and y h minus the concentration of h plus from water is 10 power minus 7 molarity the concentration of o h minus from water is 10 power minus 7 molarity and therefore for very highly concentrated solution like 10 power minus 3 molar 10 power minus 2 molar 10 power minus 1 molar the even tempo minus 4 also up to thousand you can say when wind is 100 you can always or when it is 10 power minus 6 you can always use 10 power minus 7 also okay but when 10 power minus 5 minus 4 it's going to be huge value and therefore definitely you can neglect the uh amount of x plus given by water when or while calculating ph or poh for concentrated rhetoric solution or concentrated basic solution we can neglect your concentration of x plus or yx minus given by water in the case of dilute or very dilute solution definitely h plus and o h minus contribution by water or from water should not be neglected and for the same this is the classical example i hope are you all clear children kindly madame how to take how to find anti logarithm when number is more than one like one point three four eight yeah i will tell you one point three four eight i will tell you no problem absolutely fine that's a very good question anti log of anti log of 1.348 okay antilog of 1.3480 you can assume as zero now for antilog you should consider only the numbers after the decimal so this is your a segment three four is a segment a it is b segment and c segment is zero c segment is zero now therefore what is the antilog 0.34 under 0.34 freeze the row the row is 0.34 under 0.348 under 0.348 the value is 2228 the value is 2 2 2 8 the value is 2 2 to 8 and we don't have zero value in the mean difference and therefore c segment contribution is 0 don't worry about that so under 0.34 under 8 you have got 2 2 2 8 therefore 0.2228 0.2228 this is your c segment value okay 0.2228 multiplied by 10 power multiplied by 10 power this characteristic value is what 1 add 1 to that 2 1 plus 1 is 2 1 plus 1 is 2 therefore 0.2228 multiply by 10 square point 2 2 2 8 multiply by 1 square or 10 power 2 now what are the values is 100 22.28 that is equal to 22.28 now i am going to take logarithm of 22.28 and going to prove that the value is what 1.3480 now this is a segment and this 2 is b segment this 8 is c segment okay and in your corresponding there are before the decimal there are two integers before the decimal there are two integers before the decimal there are two integers and therefore two two digit minus one two integer minus one therefore it is one point something now we have fixed the characteristic value one point something what is the mantissa under 22 under 22 you have to see the log table under 22 under 22 under 2 okay 22 under 2 will be 0.3464 22 under 2 will be 0.3464 0.3464 okay 0.3464 and then under 8 under 8 under 8 it is 15 15 15 and therefore it is 0.3479 0.3479 and therefore one point three four seven nine one point three four seven nine log of twenty two point two eight is one point three four seven nine and anti lag one point three four eight is what twenty two point two eight now you can see when one point three four seven eight is approximately equal to one point three four eight because the next digit is more than five the next after seven is more than five you can add one to seven you can add one to seven you will get one point three four eight therefore when you want to cross check whether your log calculation or anti-lock calculation is correct you do the reverse process in the reverse table you will understand the correctness anti-log of 1.38 is what 22.28 log of 22.28 is 1.3479 we have cross chat yeah i hope i have answered that 1.348 question southern krishna gupta so we can drink this molar concentration of acid yeah correct obviously you are drinking i hope you will have you will have you definitely consume coke or coca-cola or pepsi or whatever it may be and that contains carbonic acid in fact that concentration is more than this value that concentration is more than this value this is approximately equal to water value okay six point you see the ph ph is 6.9586 it's approximately water it is not acid it's approximately water it's nearly water whereas the carbonic acid watch what you drink in soda water in carbon dioxide pumped water that is pepsi or coke or cola whatever may be the drinks the aerated water and that is nothing but your carbonic acid co2 h2o is carbonic acid and that ph is much lesser than this value and you are even drinking that and why not you have this concentration you can definitely drink so is concept clear on how to calculate the ph using logarithm yes 198 96 percent no 13 4 no problem that four percent i i i am at your feet children that 13 student kindly kindly watch the video once again kindly watch the video once again post your doubt to mentor kindly watch the video once again post your doubts to mentor kindly watch your video once again post the doubts to mentor definitely we are ready to help you we are ready to help you and all the professors in our guru we are always for your doubts we are always at your service we are definitely for your service and it is your duty to contact the mentor and contact us through mentors contact us to get the doubts cleared of course in the class we are trying to clear all the doubts whatever i am getting in the chat window in a similar manner if any mentor contacts me for some specific doubt definitely all the professors will be ready to help not only my children all the other chemistry professors and physics professors and mac professors of course biology professors also they are ready to clear all the doubts and i am very happy that 198 children 96 percent are clear and 13 children they have said no i don't know why they have said no maybe they would have joined late or maybe i am little faster kindly excuse me those 13 children are four percent and i i kindly forgive me and also excuse me and definitely in the next class i will try to uh deliver much more at a better speed and better language and better conceptual clarity so that you also have the benefit of what understanding the concepts and children it's now 651 i don't think i can do one more problem now because when i start one question definitely it's going to take more time and i hope you are all clear about the logarithmic concept and ph calculation kindly using this the system of approach kindly proceed with the calculation in any of the physics or chemistry wherever required in numericals and you will be definitely appreciating the concept and you will enjoy in doing the log calculation and kindly if you have any specific doubt in doing some calculation if there is any error in the textbook or if there is any error whatever you make and not matching the answers from the textbook please kindly text to mentor mentors they will clear by themselves or if possible they will direct if necessary they will direct the doubts to us and we are ready to help you at any point of time and before winding up the class again i request you all to vibrate the words i will clear cet with a good score three times i will also pray for you all thank you children i once again request kindly send the feedback to mentors so that it will be encouraging for entire system of guru professors so that we can do much more better way in our future classes kindly give the feedback to our mentor children thank you that's all for the day bye bye enjoy your day thanks madam i will wind up the satsang man thank you