Prove, formally that: $\log_2 n! \ge n$ for all integers $n>3$.
Hint: first prove that $n! ≥2^n$, for all integers $n >3$.
So far what I have:
Base case, $n = 4$,
$4! = 24$
$2^4 = 16$.
Therefore, it is true when $n = 4$.
So how do I proceed from here?
I know I can log the whole equation which will lead to $\log_2 n!$ and $n$. But the linkage seems to be missing. Sorry for the untidiness about the math symbols. I am trying to input them correctly but apparently I am not doing it right.