1. The problem statement, all variables and given/known data Hi, I am trying to prove for a>1, b>1 that f(x) = O(log_b(x)) then f(x) = O(log_a(x)). [Hint: log_b(x) = log_a(x)/log_a(b)). 2. Relevant equations 3. The attempt at a solution Assuming |f(x)| <= C|log_b(x)| true for x>k, then, f(x) <= log_a(x)/log_a(b)| for all x>1, C=1 then, log_a(b)*f(x) <= log_a(x) all x>1 C= 1/log_a(b) f(x) <= log_a(x) x>1 C=1/log_a(b) f(x) is O(log_a(x)) Now here comes my problems with most big-O problems, since the right side is being divided by something I should just multiply it out to other side: log_a(b)*f(x) <= log_a(x) I know that log_a(b) on left side would not matter except that it might be C= 1/log_a(b) and k =1 According to my textbook/notes, C = 1/log_a(b), I still do not see why though, because if I multiply both sides by log_a(b) why C is like dividing both sides log_a(b), if someone could explain it, I would appreciate it thank you very much. Please Let me Know if this correct, thank you very much. TheLegace.