Can You Solve This Math Problem? Find x Challenge

Ajouté : 2026-06-06

[00:00:00]Very simple to solve. Watch to the end.

[00:00:03]We have 8 to the^ of x + 1 + 8 ^ of x + 2 is equal to 360. We are asked to find the value of x. Let me show how to solve this. Now we are going to expand this using the law of indices. So we shall have 8 to the^ of x * 8 the^ 1 because from the law of indices whenever you are having the same base you can what you can add the power. So if we we shall return this to the what original expression if we apply the law of indices this is plus 8 to the^ of x * 8^ 2 all of this is equal to 360.

[00:00:46]Now 8 to the^ of 1 is 8. So we shall have 8 to the^ of x * 8 + 8 ^ of x * 8 ^ of 2 is 64. All of this is equal to what? 360. So we can say let y to be equal to 8 to the^ of x. The reason why we are using this 8 um 8 to the^ of x to become y is because this is a whole thing and this is a whole thing.

[00:01:15]So you cannot solve this without using factorization or you can use substitution. So I choose sub method. So now whenever I see my x to the^ x I impute my y. So this become y.

[00:01:30]This is y. So y * 8 is 8 y. So we shall have 8 y + this is y. So y * 64 is 64 y.

[00:01:42]All of this is equal to what? 360.

[00:01:45]So if we add this, we shall have 72 y to be equal to what? 360. So if you divide both side by 72, if I divide here by 72 and divide here by 72, which means this cancel out, our y is equal to 360id 72 is 5. But our y is equal to 8 the^ x.

[00:02:08]But our y is 5. So that means our 8 to the^ of x will be equal to what five.

[00:02:15]You cannot solve this um without using log ready because you cannot set the base equal. So we shall introduce log to both side. So if we introduce log to both side we shall have um the log of 8 to the power of x will be equal to the log of 5.

[00:02:34]All right. Now watch this. From the law of logarithm, this x can multiply log 8.

[00:02:40]So we shall have our x * log 8 to be equal to log 5. Let's divide both side by log 8. So if we divide here by log 8 and also divide here by what? log 8. So this cancel out our x will be equal to the log of 5 / log 8. Is that the final answer? Let us apply this law of um logarithm. If you have the log of let me say um a base of b divided by the log of um let me say x base of b. Now this is a um a change of base which means this can be written as what? as log a base of b because this must have the same base sorry um log a base of x okay because the bases are the same. So in this place we shall apply it here. So from this law of log this become x to be equal to the log of five base of 8 because this log has a neutral base of 10. So this is just as saying log 5 b 10 log 8 b 10 they have the same base. So we apply this law which the final answer results to x to be equal to log 5 base 8. Thank you for watching.

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