I think that $n!$ grows fast than $(\log n)^n$ but how do you show that?
I'm doing a practice exam right now and I have to compare functions. Is this correct?
$28 <\log n^{2020} < 5n^{3/7} < 2^{n^{1/2}} < (\log n)^{n/2} < n! < n^n$
I know how to show everything apart from $(\log n)^{n/2} < n!$.