The Question That Stops Most Students from Going to University | Must Watch | Log 😱😱🤯😯

追加: 2026-05-12

[00:00:00]Hello everybody. Welcome to this platform. This is Sichamba Jacob and I guess each and everybody is doing very fine wherever you people are watching this video from. So we've got this question.

[00:00:14]Uh we're going to apply what we call change of base. The question reads, find the value of x.

[00:00:23]We've been given log base 4 of x plus log base 2 of x is equal to 6. So how we get to find the value of x?

[00:00:34]So it's really very simple here.

[00:00:37]Basically, what we're going to do here is uh to change the base here. And I encourage you to be taking into the smaller base.

[00:00:47]So here it'll be log base 2 over x over log base 2 of 4.

[00:00:57]This is the first step.

[00:00:59]So you just change this side, log base 2 of x over log base 2 of 4 and say plus log base 2 over x is equal to a 6. So we can see that we've got base 2 here, base 2 right over here and base 2 here.

[00:01:20]So in case you are wondering how we change the bases, this is how it works.

[00:01:26]So mostly, what we normally do here when you've got log base a of b and you want to change this to base c, you just say log base c of what is here, that is b, over log base c over the base which is here, which is a. So this is what we normally do whenever we want to change the bases. And it's what I've applied right up here. So I said log, I'm taking it to base 2 of x over log base 2 over the 4 which is right here.

[00:02:07]So that's it. Now from this point of course from this point what we're going to do is to simplify right here on the denominator.

[00:02:19]So we've got uh log base 2 of 4.

[00:02:25]This can be written as log base 2 of 2 power 2.

[00:02:31]We know of course that uh 2 power 2 will give us a 4 and this is the advantage that we've taken.

[00:02:39]So in logs, since the base is equal to this base, you can cancel them out and you remain with a 2, which is right here. So meaning, whatever we have right here is equal to what? Is equal to a 2.

[00:02:53]So we can write down here that we've got a 2 here.

[00:02:58]I want you to see. So this is a a 2.

[00:03:03]And now, since we've got a 2, we can now solve this.

[00:03:08]And solving this we can either let or just go direct by solving. So let me let me just do some let here. We're going to say let let, okay, y be equal to log base 2 of x.

[00:03:29]So we're just letting this log base 2 of x and this also log base 2 of x be equal to y.

[00:03:36]So once we do that, we can say y over 2 plus y is equal to 6.

[00:03:45]So this is a 2 here. So y over 2 plus y because we said let it be equal to y.

[00:03:53]And there is nothing much or nothing that is complicated. The reason why I've let it be equal to y. If you want to you can go with it the way it looks. Or if you want to let it be equal to any letter so that it's very easy for you to to to work out.

[00:04:08]So now here we can find the lowest common denominator. In our case, it's a 2. 2 into 2 it's a 1. 1 times y it'll give us a y.

[00:04:20]Plus there is a 1 here. 1 into 2 it's a 2. 2 times y that is a 2y, which is equal to a 6.

[00:04:29]We can add these like terms. We're getting a 3y over 2, which is equal to a 6.

[00:04:36]So we cross multiply.

[00:04:38]This of course will give us a 3y is equal to a 12. We divide here by 3 by 3.

[00:04:47]The value of y is coming out to be equal to a 4. So the value of y in our case it's equal to a 4.

[00:04:55]So now, what we do with this 4? Remember we said y is equal to what? y is equal to log uh base 2 of x. Now we know that the value of y is equal to a 4, which we've just found here. So what we can do here is to substitute back. So we shall say we shall say 4 is equal to log base 2 of x. So where there is y we write a 4. And from here we can solve for x. So this will be a 2 power 4 is equal to x. Remember the logs, there's a rule which I've just applied here.

[00:05:41]When you've got uh when you've got uh when you've got log base a of b is equal to c. So what we normally do to cancel or to get rid of the log we write this b the way it is and then we say equal to a comes this side and then whatever is here becomes the power. And this is what I've applied here. So this 2 has come this side and the 4 which is here becomes the power.

[00:06:09]We remain with x here. And this is giving us a 16. So the value of x is equal to a 16. Thank you so much for watching. This has been Sichamba Jacob.

[00:06:21]Please share this video. Leave a comment in the comment section and bye-bye.