Cormen 3rd edition Problem 3-2 part (f)

Question

Indicate for pair of expressions (A,B) whether A is O, o, Ω, ω or  of B?

A = lg(n!)

B = lg(n^n)

Comments

Though $n! = o(n^n)$

$log(n^n) = nlogn $

There is a result of Stirling formula : 

$log(n!) = \Theta(nlogn)$

Hence, $A = \Theta(B)$

So, $A = O(B)$, $A = \Omega (B)$