hi guys hi guys hi guys hi guys hi guys it's me teacher in today's video hi guys it's me teacher going in our today's video we will talk about how to solve simple logarithmic equations last time we have uploaded a video where in we discuss about the development functions and on today's topic method will focus on solving logarithmic equations so without further ado let's do this topic and logarithmic function logarithmic equation and even exponential function are interconnected to each other so this time in solving simple logarithmic equations we will apply our knowledge on how to convert logarithmic equations to exponential form casino on how to find the missing term or the missing variable in these given examples so we have here item number one two three four and five and right after this discussion i will upload two more videos param guaranteeing leveling when it comes to the discussion on how to solve logarithmic equations let's start with item number one we have here the logarithm of 16 to the base of 2 is equal to x so again as i have mentioned earlier we will use our knowledge on how to transform this logarithmic form into exponential form for us to solve them so to solve them using x using the exponential form we will convert this remember this is your base your base 2 will be raised by x is equal to 16. again what you will do we have 2 raised to x is equal to 16 again 2 raised to x is equal to steel so that is the first step on how to solve that kind of logarithm now sir how how can you solve for the value of x and the number of guys is you need to express them into the same base if the base of this one is 2 with its point of x we need to express 16 in which the base will be equal also so we have here 2 raised to x is equal to we know that 2 raised to 4 is equal to 16. therefore we can replace 16 by 2 raised to 4. and as you can see guys as you can see we can solve them we can all we can simply equate their exponent in which your x is equal to four this is the answer for it okay so the question simply guys yes sir how can you check whether the answer is correct that's pretty checking guys as for the checking you can have the logarithm of 60 to the base of 2 is equal to your x which is 4 and then converting this this will become 2 raised to 4 is equal to 16. as you can see when you simplify 2 raised to 4 that is also equal to 16. so pares and more so again um the key here is to transform the given equation in exponential form or the given logarithmic equation in exponential form now let's move on with item number two if you know how to do this you can pause the video and then try solving it and we will do this in our way so let's try number two we have logarithm of 27 to the base of x is equal to three so first thing you need to do is to write this so as you can see this one is quite different so again this is your base x raised to 3 so we have x raised to 3 is equal to 27 okay x raise 3 is equal to 27 now what will happen here is that as you can see guys this one is raised by three so you will think how how are going to solve this one we know that 27 is equal to 3 raised to 3 right so we can have here x cubed is equal to 3 raised to 3. as you can see the exponents are equal therefore the bases are also equal so we have here x is equal to three the value of x in item number one is simply three now let's have item number three for item number three we have the logarithm of x the base of five is equal to three as you can see a placement and variable extent here we have after the equal sign your base is x and here you argument that your ex different encounters our bahama players such as different problems may encounter yes so we have here again the logarithm of x to the base of five is equal to three so first thing you need to do is to convert this into exponential form we're in your base 5 to the power of 3 so we have 5 raised to 3 is equal to x we have is equal to x so again let me repeat my conversion from logarithmic form to exponential form 5 raised to 3 is equal to x and to find the value of x all you need to do is to simply simplify 5 basically we know that your exponent indicates how many times you will multiply the base by itself if this 5 raised to 3 it will become 5 times 5 times 5 is equal to x and 5 times 5 is 25 times 5 that will give you 125 as the value of x and this is our answer for item number three you need to know the conversion and you know how to manipulate the given expression or even use the loss of exponents okay let's move on with item number four we have the logarithm of x base of 32 is equal to four over five so what you will do here is to convert again and then you will convert this fraction you will convert this into exponential form we have 32 raised to 4 over 5 is equal to x again 32 raised to 4 over 5 is equal to x so to find the value of x um since this one is a fraction of fractions we know that we can express 32 as 2 raised to 5. check we have 2 times 2 times 2 times 2 times 2. this is equal to 4 okay this is equal to 4. so we have now 16 and then times two that will give you the answer of 32. so again you can express 32 be equal to 2 raised to 5. sorry bracket 4 but if it is brand it was included guys since we need to eliminate 5 is it in a bio number that you can express into an exponent of time and that is 2 so we have now 2 raised to 5 times four over five tomorrow we are again you will multiply their exponents okay so you can cancel out five at this denominator and all you have here is equal to x okay so i will explain uh one by one young thirty two nineteen is equal to two raised to five and then my original exponent which is four over five is equal to x exponent a power power of a power wherein if you have an exponent here and exponent outside the parenthesis you need to multiply them so what happened here is that you have 2 raised to 2 a raised to 5 times 4 over 5 and multiplying them are simply a cancellation then equal to x but you have 2 raised to 4 and that is equal to x 0 we're not yet done guys we need to simplify 2 raised to 4 in which 2 is 4 is equal to how many 16 and your value of x is equal to 16. that's it guys when it comes to the loss of exponents guys let's move it with item number five we have the logarithm of two x plus one to the base of two is equal to three and whatever don't worry this is the process first find binomial uh you need to express it into exponential form so we have here two raised to three okay is equal to 2x okay so we have 2 raised to 3 is equal to 2x plus one so as you can see guys um and that really is you need to simplify this and you can have a new equation what is 2 raised to 3 2 is 3 is equal to a so we have now a is equal to 2x plus y and then manipulate your equation you can transpose this to the other side in which when you transpose this when you transpose this it will change the expression you have or that sign we have 8 minus 1 is equal to x now simplifying this will give you 7 is equal to 2x and to solve for x divided by both sides by 2 cancel cancel your x now is equal to 7 over two so is it okay if we express our answer in a fractional form yes now if you want to check uh guys if you want to check if you want to check are we not in the loganithm of 2 times for x which is 7 over 2 plus 1 to the base of 2 is equal to three we're in couple of special exponential form two raised to three is equal to eight and we know that two raised to three is eight so we have now an equal equation so in this opinion guys the answer of seven over eight yes is the correct answer in solving this okay so let me erase this anyhow guys i hope that you learned something from this simple video on how to solve simple logarithmic equations so if you if you have any question about this feel free to comment down below at kumeronkayon requested a topic that you wanted to discuss your inside in comment section so by the way guys uh we i will also upload a part two of this video we're in we will solve uh logarithmic equations where in we will apply laws of logarithms so if you're new to my channel don't forget to like and subscribe but it hit that little bell button for you to be updated sucking latest uploads again it's meet you for going bye you