I am trying to to #3(b) from the attached image and I don't know how to go from the f'(x) = stuff part to the the "Since ln(2) > 1/2" part and the stuff that follows it. I don't get the logic there. I do understand the decreasing for x >= 2 stuff and how to deal with the inequalities algebraically but, like mentioned, I just don't get why I'm going directly from f'(x) = stuff to "Since ln(2) > 1/2".

Any help would be greatly appreciated!

Thanks in advance!