Expert: Paul Klarreich - 12/18/2009

Question
Dear Sir,

So for as we have read lograthims formulae as follows.
log(a.b) = log a + log b
log(a/b) = log a - log b  (considering base as 10)
But what for
log( a^x + b^x) = ???????
I mean how to solve questions like
2^x + 9^x = 92 using log????

If we take log both sides then

log(2^x + 9^x) = log 92
here the main problem rises how to open left side of above equation?????
Is there any formula??

Please guide me.

Thanks in advance.

Answer
Questioner: Rashid Mehmood
Country: Pakistan
Category: Calculus
Private: No
Subject: Logrithms
Question: Dear Sir,

So for as we have read logarithms formulae as follows.
log(a.b) = log a + log b   << OK
log(a/b) = log a - log b   << OK, and true for any base
But what for
log( a^x + b^x) = ???????
I mean how to solve questions like
2^x + 9^x = 92 using log????

If we take log both sides then

log(2^x + 9^x) = log 92
here the main problem rises how to open left side of above equation?????
Is there any formula??
...............................
Sorry, there is no logarithm property for this.  Logs are not good for sums or differences.

Usually you just need inspiration. (I don't have any for you.)