I cant understand why we get log n while solving recurrence of Merge Sort. I have attached the book content. It replaces the ' 1 ' on RHS by log n. It says" because all of the other terms cancel & there are log n equations and so all the 1s at the end of these equations add up to log n."

If n is 8, then we would split list into 4, 2 and 1. This means that there would be 3 equations, but log 8 is not 3 mathematically.

Can some body please explain me the number of equations for n=8?

Zulfi.