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
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