High Quality Content by WIKIPEDIA articles! In mathematics, specifically in abstract algebra and its applications, discrete logarithms are group-theoretic analogues of ordinary logarithms. In particular, an ordinary logarithm loga(b) is a solution of the equation ax = b over the real or complex numbers. Similarly, if g and h are elements of a finite cyclic group G then a solution x of the equation gx = h is called a discrete logarithm to the base g of h in the group G.