Find the solution set of in
Remember the following rules of logarithms: for and ,
Firstly, we consider what values of the equation is valid for: this equation is valid when both and , hence when . Now, to solve the equation we apply the power rule of logarithms (rule 1 above) then we apply the multiplication rule for logarithms (rule 2 above), then we solve for .
Expressing this equation in exponential form gets us
Therefore, and the solution set of the equation is .