1. The problem statement, all variables and given/known data If a differentiable function f(x) satisfies the equation f(xy) = f(x) + f(y), prove then that f(x) = alnx. 2. Relevant equations 3. The attempt at a solution I have proved that if f satisfies f(x + y) = f(x)f(y) then f(x) = 0 or f(x) = e^(ax) and I also know that if a function f satisfies f'(x) = af(x) for some constant a, then f(x) = ce^(ax) for some constant c and a.