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

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

what if c > log(n) ?

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

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 $n$.


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