Time complexity comparison

Question

I'm struggling with these 2 questions:

What are the relations $(\mathcal O, \theta, \Omega)$ :

$\quad\text{a.}\,$ $\log(n!),n\log(n)$

$\quad\text{b.}\,$ $\ln\left(e^{e^k}\right)^{\displaystyle\ln(\ln e^{e^k})},e^{e^k}\cdot\ln\left(e^{e^k}\right)$

I'm trying to understand what should i prove here and what is the approach for solving that?

Q1: both expressions are O(nlogn) ? Q2: ??

Thanks.

Answer 1

The first two are $n\log n$ for part $b$, $\mathcal{O}(e^{k^2})$ and $\mathcal{O}(e^{k{e}^k })$