<s>[INST] Equation with different bases (exponential) I seem to be stuck with the following equation right here:
$$2^x + 2^{x+1} = 3^{x+2} + 3^{x+3}$$
 [/INST] \begin{align}
2^x+2^{x+1}&=3^{x+2}+3^{x+3}\\
2^x+2\cdot2^x&=3^2\cdot3^x+3^3\cdot3^x\\
(1+2)2^x&=(3^2+3^3)3^x\\
3\cdot2^x&=36\cdot3^x\\
2^x&=12\cdot3^x\\
\left(\frac23\right)^x&=12\\
\end{align}
Now use logarithms.
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