Prime-base logarithm of order

Definition
For a group of prime power order, the prime-base logarithm of order is the logarithm of its order to base equal to the prime. In other words, for a group of order $$p^k$$, where $$p$$ is prime, and $$k$$ a nonnegative integer, the prime-base logarithm of order is $$k$$.

The number $$k$$ is sometimes a more useful size measure than $$p^k$$. It also permits more ready comparison with such measures as the nilpotency class, derived length, and Frattini length.