There are several “Laws” of Logarithms. They are:
The bases seem to cancel in the first expression and to swap with the argument in the second.
Ie we eliminate a log by raising the base to the power of both sides.
Problems involving logs usually reduce to a simple linear or quadratic equation.
Example:
Use the first rule to obtain a single log.
Use the sixth rule to eliminate the log.
Expand this and simplify.
Factorise and solve.
Example:
We must make the bases the same for both logs. We can do this with the second case of the fifth rule:
We have,
Substitute 
to give
and multiply throughout by p:
Subtract 
and simplify to give,
then factorise.
So,
or