For 10 points, name this function which is the inverse of exponentiation.
This function of  n-factorial is approximated by Stirling's formula. The number of primes less than  x is approximated by  x over  this function of  x. The Euler–Mascheroni constant equals the difference between the nth harmonic number and this function of  n, as  n approaches infinity. Up to a constant, this function is the integral of 1-(*)  over- x. This function of "x  -to-the- p" equals  p times this function of  x. This function allows one to calculate products as sums, using tables of values of it. One can use division to change the base of this function. For 10 points, name this function which is the inverse of exponentiation.
This function of  n-factorial is approximated by Stirling's formula.
logarithm function [accept more specific answers like " log base two " or " natural log arithm"]