This function applied to a negative real number has an imaginary component of i times pi.
The probability that a random integer n is prime is approximately the reciprocal of this function of n, according to the prime number theorem. This function of n factorial is close to n times the quantity negative one plus this function of n by Stirling's approximation. This function applied to a negative real number has an imaginary component of i times pi. The slide rule uses the fact that this function of the product of two numbers is the sum of this function applied to both numbers. This function's derivative is equal to one over X. For 10 points, name this function, the inverse of exponentiation, whose "natural" form uses the base e.
The probability that a random integer n is prime is approximately the reciprocal of this function of n, according to the prime number theorem.
{log}arithm [accept natural {log}arithm or {log}arithm base e; accept “logarithmic integral” until “n factorial”]