How do I work out the last sentence in this section of a proof of the Unique Factorization Theorem?

Question

The last sentence states that the number of possibilities is $2\log_2 n$ (see the below image to follow the proof). I don't understand how to get $2\log_2 n$ but I understand everything that comes before it. Can someone elucidate this reasoning for me?

Thank you.

Answer 1

I believe that all this is saying is that $1+\log_2 n\le 2\log_2 n$ for all $n\ge 2$ - this is trivial because $\log_2 n \ge 1$ for all $n\ge 2$.