# help please - powers/log question

• October 1st 2012, 06:46 AM
razidan
Hi all,
This question appeared in a logarithm chapter.

(√(4+√15))^x + (√(4-√15))^x = 8

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

Raz.
• October 1st 2012, 07:03 AM
Plato
Re: help please - powers/log question
Quote:

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

By inspection $x=2$.
• October 1st 2012, 07:45 AM
razidan
Re: help please - powers/log question
Can I see the full solution please?
• October 1st 2012, 07:59 AM
Plato
Re: help please - powers/log question
Quote:

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.
• October 1st 2012, 08:27 AM
razidan
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...
• October 1st 2012, 08:36 AM
Plato
Re: help please - powers/log question
Quote:

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?
• October 1st 2012, 02:16 PM
razidan
Re: help please - powers/log question
Attachment 25000

number 4.30
• October 1st 2012, 02:41 PM
Plato
Re: help please - powers/log question
Quote:

Originally Posted by razidan
Attachment 25000
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.