Will the inequality log M ≥ C*log 2 always hold, where M is a positive integer and C is the number of distinct prime numbers that divide M?
If so, prove it.
If not, give an example.

(In reply to re: solution by Ady TZIDON)

I see that now that you point it out. The equality holds for M = 2^n for only n= 0 or 1; no other values of n. For every other M, including 2^n for larger values of n, it is the inequality (greater than).

Posted by Charlie on 2015-03-18 07:52:22