Help w/ an exponential equation

How would I solve exactly for 'x' without using a calculator in the following equation?

3^(2x)=5^(x-1)

I cannot seem to think of any possible way. Any help would be appreciated.

use any logarithm you want, for example, natural:

ln ( 3^(2x)) = ln (5^(x-1))
2x ln (3) = (x-1) ln(5)

expand:

2x ln(3) = x ln (5) - ln (5)

substract x ln(5) from both sides:

2x ln(3) - x ln (5) = - ln (5)

multiply by -1 and factorice:

( ln(5) - 2 ln(3) ) x = ln (5)

simplifying:

(ln (5) - ln (3^2) ) x = ln(5)
(ln(5) - ln(9) ) x = ln(5)
ln (5/9) x = ln(5)

x = ln(5) / ln (5/9)

I hope there is no mistake...

Just reinforcing Rock Lee's answer. I had homework like that a few nights ago, that worked for me.

that's if X is real... if X is complex, then it's another story... (I think you wanted just the real one right? If not, I can find them, just ask)