In this work, we present an algorithm for computing logarithms of positive real numbers, that bears structural resemblance to the elementary school algorithm of long division. Using this algorithm, we can compute successive digits of a logarithm using a 4-operation pocket calculator. The algorithm makes no use of Taylor series or calculus, but rather exploits properties of the radix-d representation of a logarithm in based. As such, the algorithm is accessible to anyone familiar with the elementary properties of exponents and logarithms.