Solve $n^4>3^n$ $n^4>3^n$
I'm trying to solve this inequality problem, but everything I can find online is either how to solve log inequality problems or exponent inequality problems.
I think this may be a combination of both of them, but I can't figure out how.

Not an answer (in view of the other ones), just a suggestion for future work.
Most questions of the form:
$$m^n<?>n^m$$
are quickly addressed as equivalent to:
$$m^{\frac{1}{m}}<?>n^{\frac{1}{n}}$$
which is addressed by the behavior of:
$$f(x)=x^{1/x}$$
in its domain $(0,+\infty)$, with care to be taken at $x_0=e$.
