In general, finding exact solutions of exponential or logarithmic equations can be very difficult (if not impossible). There are several common strategies we can try.
Some kinds of logarithmic and exponential equations can be solved by appealing to the one-to-one properties of logarithms and exponentials:
Use logarithms and their properties to reduce an exponential equation to a simpler equation.
Use exponentials and their properties to reduce a logarithmic equation to a simpler equation.
Use algebraic techniques such a factoring, common denominators, etc.
If an exact solution can be found, some combination of the above strategies will probably be helpful.