<s>[INST] Solve the equation $$9^x=5^x+2\sqrt{20^x}+4^x$$
I'm not really sure where to start. I tried simplifying with logarithms and factoring out the x but it ended up looking just as complicated..
 [/INST] \begin{align*}
9^x&=5^x+2\sqrt{20^x}+4^x\\
9^x-5^x-4^x&=2\sqrt{20^x}\\
 \text{At this point, one solution jumps out}&\\
9^2-5^2-4^2\space 
=\space 81-25-16\space 
=\space 40&=2\sqrt{20^2}\\
\implies x=2
\end{align*}
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