<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] Note that $2^x+2^{x+1}=2^x+2\cdot 2^x=3\cdot 2^x$.
Similarly, $3^{x+2}+3^{x+3}=9\cdot 4\cdot 3^x$.
So our equation can be rewritten  as $3\cdot 2^x=9\cdot 4\cdot 3^x$, or equivalently $(3/2)^x=1/12$, which can be solved using logarithms.
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