1. The problem statement, all variables and given/known data (Here, by 'log' I mean natural logarithm) Solve for x: a.log(x) + b.log(1-x) = c for a, b and c constants 2. Relevant equations 3. The attempt at a solution Hi everyone, This is so embarrassing but this is really stumping me! I know how to do it if a=b: a.log(x) + a.log(1-x) = c log(x) + log(1-x) = c/a log(x(1-x)) = c/a x(1-x) = exp(c/a) and then you get a quadratic in x which you can solve. However, I can't work out how to solve it if a is not equal to b, as I can't see how to group up the logs nicely without ending up with horrible powers of x. What direction should I go in? Thanks for any help!