Hello friends Meet again with my brother on the legurless channel in this video in this series we will learn about equations and exponential functions in this series we will learn various forms of exponential equations How do we process an exponential function until later we draw a graph of an exponential function so don't forget to like the video and also to subscribe to the gurless channel and later on the top right I will give you a link to a collection of videos about equations and exponential functions so that friends can learn from the first video to the last video before we continue watching the video I want to tell you that now you can become a member on the legruless channel there are three levels of membership that you can get, namely the linear quadratic and cubic levels of course each has its own advantages that you can get you can become a member by clicking the join button on the bottom right of the video or on the leg grules channel page Congratulations on joining now let's go straight to the first form so this is the basic form of an exponential equation the first form or basic form is a^ FX yes FX is a function in x = a^ at p where p is a number can be a number integers can be fractions can be root numbers yes later we will see some examples of questions involving various forms of numbers now How do you solve it in leaving an exponential equation in a basic form like this when the base number is the same a yes then we can say the solution or X that can satisfy this equation is FX = P like that so later we will look for the value of x so that later the equation will be true let's just not be confused in the first example here Brother has 3 ^ 3 3X - 2 = 3 ^ 4 we see the base number is the same yes this then we can immediately say 3X - 2 = 4 so that 3x = 4 + 2 then 3x = 6 then the x is 6 / 3 that is the x is 2 so What does this mean if we put the value of x into the equation that is on the left power We will have 3 ^ 6 - 2 that is 3 ^ 4 so later on the left 3 ^ 4 = 3 ^ 4 yes the result is the same left is the same right so the equation becomes true Well that's what we find the value of x that we are looking for so that the left equation is equal to the right Well, what if it turns out that the base numbers are different, for example here we have Du 4x + 1 = 8 ^ 1/3 if the base numbers are different then friends have to see first maybe we can make the base numbers the same in the case of this example problem we have 2 ^ 4x + 1 where 8 is 2 ^ 3 yes 8 is 2 ^ 3 means we have 2 ^ 3 then raised to the power of 1/3 again means here friends must already be able to basic exponents, namely the properties of the exponent exponent number raised to the power again means we have later 2 ^ 1 Get from 3 * 1/3 yes this is 1 = 2 ^ 4x + 1 now the base numbers are the same if the base numbers are the same we can immediately see the exponents so that it is correct then 4x + 1 = 1 then 4x = 0 0 x is 0 / 4 we have 0 it turns out the value of x must 0 so that this equation becomes true Well that is the basis for the first form let's try some examples of the following questions here we have 10^2x - 3 but we have 1,000 here remember 1000 we can write as 10^3 so that if it is the same number The main thing we can see the power 2x - 3 = 3 then 2x = 3 + 3 because the -3 moves to the right so 2x = 6 so the x is 6 Dib 2 that we have is 3 means the value of x that makes this equation true is 3 we try the number two the main number is now different again even there is a fraction no need to be afraid let's check maybe once again the number 243 can be expressed in 3 powers what on the left we have 3^x² - 6x = 1/243 if we divide 3 into 81 yes this is 9 * 9 or 3 * 3 here Well that means 243 is 3^5 Now we have the 3^ 5 but it can't be below it must be both above it then we have 3^ x² 6x = 3^ -5 using the properties of exponents yes 1/a^ n we can write as a^ -n if it's the same base number we just look at the exponent then x² - 6x = -5 x² - 6x equals 5 = 0 yes Sis Write on the right x² - 6x + 5 = 0 here means the form is a quadratic equation yes Sis I hope my friends still remember the forms of quadratic equations taught in junior high school class yes means How to do it we want to find how many times how many the result is + 5 which if added the result is -6 yes what is multiplied the result +5 is can be 5 * 1 yes means -5 * -1 then -5 + -1 the result is -6 so we can factorize this form as x - 5 * x - 1 = 0 means x - 5 = 0 or x - 1 = 0 yes means X = -5-nya moves to 5 and here X becomes 1 means here we can write the solution set of equation number 2 is 1.5 This means there is X x can be 1 x can also be 5 it's quite easy if there are fractions What if there are roots well it's actually the same huh Hey there there is another addition subtraction Sis Well this is not allowed we have to force this to move to this side for the other one first yes the other one we have here -2x + 2 if there is a root friends can raise the power set / 2ah remember if we have a this is a ^ 1 / 2 1 is the power inside 2 is the power of the root or friends can write as the one inside is raised to the power of 12 is the same as this move here So 625 this is 25 25 means 5 ^ 4 because 25 is 5 * 5 yes 5 There are 4 well if it's like this it means this power can be multiplied by this power we have 5 ^ - x + 1 = 5 ^ 4 is the same as the base number means -x + 1 = 4 means later -x = 4 - 1 -x = 3 then x is -3 easy yes So the point is the base number is the same let's try this again yes wow here there is now divided yes divided this number there is another power here there is another root yes How should we Min we force it so that the form is a^ FX = a ^ b like this yes we can divide first division of numbers to powers means we have 3^-1 - x + 2 yes because this later -1 - x - 2 raised to the power again 2 equals this 1/9 that can be brother Write it down if you are confused yes let 's just do it slowly so 1/3^ 2 which is on this side if we do this becomes -x + 1^ 2 = √^ 3 from 3^-2 Okay up to here it's still okay yes This goes up this number to the power raised to the power means we have 3^ -2x + 2 is the same as this means 3^ -2 1/3 Well that means we will have 3^ -2x + 2 = 3^ -2/3 the base number is already the same means -2x + 2 = -2/3 we can multiply by 3 so that the 3 disappears -6x + 6 = -2 means -6x = -2 - 6 -6x X = -8 nega e means we can directly x yes means -8 / -6 That means we have 4/3 it turns out the solution set that satisfies it is 4/3 n easy yes finally we try the last question here is equal to 1 sis wow what if it is equal to 1 there is a trick if we find an equation that is equal to 1 we have to remember any number raised to the power of 0 the result is 1 so for this question we can really do it Yes no need for 64 we break it into 2 powers what we just write down this is 64^0 Why because if any number is raised to the power of 0 the result is 1 yes So now the base number is already the same we just use or see the power x^ 2 - 4x - 12 = 0 we can factor how many times how many the result is -12 which if we add the result is -4 well if we use 3 and 4 we can't get it we have to use 6 and 2 so to get -4 the negative is at 6 then we have -6 * 2 -12 is right which means we will have x - 6 Ah this is x + 2 = 0 means x - 6 = 0 or X + 2 = 0 means x = 6 this x = -2 means the solution set is -2.6 well something like that Thank you to friends who have watched this video Happy learning If friends find this video useful Let's share it with other friends so that more and more people can benefit from the legurless channel don't forget to like this video subscribe to the leges channel and also follow the leg ruless Instagram Thank you see you in the next videos