# Math Help - help please - powers/log question

1. ## help please - powers/log question

Hi all,
This question appeared in a logarithm chapter.

(√(4+√15))^x + (√(4-√15))^x = 8

i simply can't crack it...
thanks,

Raz.

2. ## Re: help please - powers/log question

Originally Posted by razidan
Hi all,
This question appeared in a logarithm chapter.
(√(4+√15))^x + (√(4-√15))^x = 8
By inspection $x=2$.

3. ## Re: help please - powers/log question

Can I see the full solution please?

4. ## Re: help please - powers/log question

Originally Posted by razidan
Can I see the full solution please?
So far as I know, there is no simple solution other than by inspection.
I also think that is the whole point of this question.
I have seen hundreds like it.

5. ## Re: help please - powers/log question

Really? I would guess they want me to somehow translate it into a logarithmic equation, that's the whole purpose of that chapter...

6. ## Re: help please - powers/log question

Originally Posted by razidan
Really? I would guess they want me to somehow translate it into a logarithmic equation, that's the whole purpose of that chapter...
Well did you post it correctly?
Is it product and not a sum?

number 4.30

8. ## Re: help please - powers/log question

Originally Posted by razidan

number 4.30
I see you posted correctly.
Then it is just a poorly constructed problem if you are expect to use any method other than inspection.

It is no different from solving $16^x+9^x=25.$ There is no elementary algebraic solution.