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.

Set $f(n) = n^4/3^n$. Then 
$$\frac{f(n+1)}{f(n)} = \frac{1}{3}\left(1 + \frac{1}{n}\right)^4 < 1$$
for $n\geq 4$. Thus $f(n)$ is decreasing for $n \geq 4$. Since
$$f(8) = \frac{8^4}{3^8} = \left(\frac{\sqrt{8}}{3}\right)^8 < 1,$$
it follows that $f(n) < 1$ for all $n\geq 8$. The remaining cases can be checked by hand.
