How to solve this powers problem

This equation was posted up by OnlyMath but got deleted because he posted 3 problems in 1 thread. He has not reposted it so I am because I'm curious as to how to solve it.

$\displaystyle \displaystyle{2(4^x) + 6^x = 9^x}$ Find x.

I already know the answer is:

$\displaystyle \displaystyle{x = \dfrac{log2}{log(\frac{3}{2})}}$

$\displaystyle \displaystyle{x \approx{1.70951}$

I have tried really hard to try and solve it, but I get stuck because there is a plus between the powers.

I can't go $\displaystyle \sqrt[x]{-6^x}+\sqrt[x]{9^x}$ because it doesn't work. You have to go $\displaystyle \sqrt[x]{-6^x + 9^x}$ which doesn't help in solving x.

Can someone show me a step in the right direction?