<s>[INST] How to solve $5^{x + 1} = 3^{x + 2}$ 
Solve $5^{x + 1} = 3^{x + 2}$.

I got this far, but I'm not sure how to continue:
\begin{align}
5^{x + 1} &= 3^{x + 2} \\
(5^x)(5^1) &= (3^x)(3^2) \\
5(5^x) &= 9(3^x)
\end{align}
Where do I go from here?
 [/INST] Your equation is equivalent to
$$\left(\frac{5}{3}\right)^x = \frac{9}{5}$$
Therefore, $x = \text{log}_{\frac{5}{3}} \frac{9}{5}$.
</s>