text: The computationally challenging "discrete" form of this function is used in many cryptographic tools.
full_question: The computationally challenging "discrete" form of this function is used in many cryptographic tools. As N grows to infinity, the number of digits needed to represent N experiences a type of growth named after this function. This function of "1 plus X" yields the Mercator series, which becomes the alternating harmonic series at "x equals one". The derivative of one form of this function equals "1 over x", and use of this function was first promoted by John Napier. This function is the inverse of exponentiation.  For 10 points, name this function whose "natural" version has a base of e.
first_sentence: The computationally challenging "discrete" form of this function is used in many cryptographic tools.
raw_answer: logarithm [accept any type of logarithm such as base 10 logarithm or natural logarithm; accept ln]