<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] Use natural logarithm:
$$5^{x+1}=3^{x+2}$$
$$\begin{align}&\implies (x+1)\ln 5=(x+2)\ln 3 \\
&\implies x\ln 5+\ln 5=x\ln 3+2\ln 3 \\ 
&\implies x(\ln 5-\ln 3)=2\ln 3-\ln 5 \\
&\implies x=\frac{2\ln 3-\ln 5}{\ln 5-\ln 3}. \end{align}$$
</s>