Determine the solution set of the equation in .
Remember the following rule of logarithms: for and ,
Firstly, we need to consider what values of the equation we need to solve is valid for: this equation is valid when both and . Now, to solve the equation, we apply the multiplicative inverse rule of logarithms, then rearrange.
Note: the equation is now in the form of a quadratic of . Hence, we can solve this by factorising.
Therefore, the solution set of the equation is .