The Laws of Logarithms

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.


Use the first rule to obtain a single log.

Use the sixth rule to eliminate the log.

Expand this and simplify.

Factorise and solve.


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 giveand multiply throughout by p:

Subtract and simplify to give,then factorise.



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