Does there exist an $x$ such that $3^x = x^2$? I tried solving for $x$ by using $x \log(3) = \log(x^2)
$$\log(3) = \frac{\log(x^2)}{x}$$
I'm stuck on this part. how do I isolate $x$ by itself?
Any help would be appreciated.

The unique real solution is $$-2 \dfrac{W(\ln(3)/2)}{\ln(3)}$$
where $W$ is the Lambert W function.  There are also complex solutions, corresponding to the different branches of $-2 \dfrac{W(\pm\ln(3)/2)}{\ln(3)}$
