Help with a solution about entropy!

Question

I'm triying to solve this question question, but I don't understand why $$ -\log_2 (2\pi n pq)/(2n) $$ transforms into $$O(\ln n/ n)$$ can you help me please :( !!

Answer 1

Use that $\log ab=\log a+\log b$ and $\log_b a=\dfrac{\log a}{\log b}$. Here $\log$ is the natural logarithm. Remember you want to show there exists $C$ such that your expression in absolute value is $$\leq C\frac{\log n}n$$