How to solve this type of logarithm question

Hinzugefügt: 2026-05-26

[00:00:00]You see this question? It's very, very simple. Let me tell you what you do.

[00:00:04]Solution.

[00:00:06]You This is logarithm and you are required to solve log log 32 base 8 is equal to X plus 2.

[00:00:14]Just apply this law.

[00:00:17]If you have log B base A is equal to X.

[00:00:22]The law states that if you want to remove this logarithm so that having this is what you will do is to exchange these two like this. So, X will come here.

[00:00:34]And then B will go where you have X.

[00:00:37]Then, what we have now is indices, not no more logarithm. So, if we do the same thing here.

[00:00:42]So, what we are going to do now is to remove this log here that we should have here.

[00:00:46]What we are going to do is to interchange these two.

[00:00:50]So, what do I do? What do I mean there?

[00:00:52]I'm going to have 8. This X plus 2 will come here.

[00:00:56]X plus 2 is equal to 32 will come here.

[00:01:01]Is equal to 32.

[00:01:03]Then, when you are at that point you know the next thing you are supposed to do.

[00:01:07]That is making the base of this one and this one to be equal so that I can equate the exponents.

[00:01:14]So, 8 is 2 raised to power 3 because you can multiply 2 three times to give you 8. I have 2 raised to power 3. Remember it has power X plus 2. This is equal to 32 is 2 raised to power 5.

[00:01:27]At this point you can see that the bases are now equal. And therefore, the exponents are also equal. So, what we have at the exponents is 3X plus 3 X plus 2 in the bracket is equal to 5.

[00:01:40]So, let's open the bracket. 3 * X is 3X.

[00:01:43]3 * 2 is 6. This is equal to 5.

[00:01:47]Then we are looking for the value of X. Let's collect like terms.

[00:01:52]6 will come here.

[00:01:54]So, that we are left with only 3X here.

[00:01:57]3x.

[00:01:58]So you have five plus six will cross over the quality becomes minus six. So 3x is equal to five minus six is minus one.

[00:02:06]Then the coefficient of x here, the coefficient of x is three. So for you to get the value of x, you have to divide both sides by the coefficient which is three.

[00:02:15]Divide this one by three.

[00:02:16]And you have as your final answer x is equal to minus one over three.

[00:02:23]Thank you.