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

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) ?

• For the future (and past questions) please transcribe images into text or LaTeX. Thank you. – Evil May 1 '17 at 4:31

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 $n$.