How is $ n^{log(n)} > n^c $ always for any c?

Question

I was going through the questions in MIT quiz : Question 2 g and I found this

How is $ n^{log(n)} > n^c $ always for any c ?

what if c > log(n) ?

Answer 1

In these exercises, you are asked to compare functions only according to their asymptotic behavior.

In this case, $c$ is a constant function of $n$, while $\log(n)$ is a function of $n$ that approaches $+\infty$ when $n$ becomes large.

So, $c > \log(n)$ can only hold for finitely many values of $n$.