## Logarithms

It is helpful to state the rules of logarithms:

(1)

(2)

Ifthen(3)

(4)

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

then(6)

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

Example:

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