TITLE: Solve equation with $x$ in the exponents
QUESTION [7 upvotes]: How can I solve 
$$8(9^x)+3(6^x)-81(4^x)=0 $$
for $x$ using elementary methods.
Thanks a lot!

REPLY [4 votes]: Building on @Cameron Williams' method, we divide the original equation by $4^x$ and obtain:
$$8u^2 + 3u -81 = 0$$
where
$$u=\left(\frac{3}{2}\right)^x$$
Once you solve it for $u$ then, $x=\frac{\ln u}{\ln(3/2)}$