1. The problem statement, all variables and given/known data I need to know the greatest n for which n! is greater or equal to x, and the greatest n for which nlgn is greater or equal to x. 2. Relevant equations Can't think of any. Sorry! 3. The attempt at a solution For a "normal" function, like, say, lgn or n^2, it would be as easy as inverting the function and getting n on its own, like this: lgn = x n = 2^x (where lg is of base 2) or n^2 = x n = sqrt(x). However, for n!=x and nlgn=x I can't come up with a way to do this. Help!