<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] Notice, $$2^x+2^{x+1}=3^{x+2}+3^{x+3}$$
$$2^x+2\cdot 2^x=3^2\cdot 3^x+3^3\cdot 3^x$$
$$2^x+2\cdot 2^x=9\cdot 3^x+27\cdot 3^x$$
$$3\cdot 2^x=36\cdot 3^x$$ $$\frac{3^x}{2^x}=\frac{1}{12}$$
$$\left(\frac{3}{2}\right)^x=\frac{1}{12}$$
$$x\ln\frac{3}{2}=-\ln 12$$ 
$$\bbox[5pt, border:2.5pt solid #FF0000]{\color{blue}{x=-\frac{\ln 12}{\ln(3/2)}}}$$
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