There is an axiomatic approach that defines a logarithm as any function f(x) such that f(x•y) = f(x) + f(y). But it's easy to prove that this reduces to the usu

There is an axiomatic approach that defines a logarithm as any function f(x) such that f(x•y) = f(x) + f(y). But it's easy to prove that this reduces to the usual definition for logarithms on the real numbers.