Logarithm Properties Does $$\log_{a^2}x=\log_a 2x$$
If it does, then how would you prove it?
If it doesn't, then how would I simplify $\log_{a^2} x$ so that it is in the form of $\log_a n$ where $n$ is some polynomial?

We have
$$
\log{_{a^2}}{x}=\frac{\log x}{\log (a^2)}=\frac{\log x}{2\log a}=\frac12\log{_{a}}{x}=\log{_{a}}{(x^{1/2})}\ne \log{_{a}}(2x)
$$ in general.
