It is helpful to state the rules of logarithms:





If b=x then bases seem to cancel giving(5)


These rules may be used as shown in the following examples.

Example: Solve

Rule (2) gives

The numerator and denominator both factorise to giveand we can cancel to give

Rule (6) now gives


Rule (2) gives

Rule (3) givesso we have

We have a log equation with two bases so we must use Rule (5) to make the bases the same.

The equation becomes

Rule (3) gives

We can now group the lnx terms:

Now use rule (6) to give