
The Logarithm Rules
You can change the base of the log using the following formula:
Example 1 – Write the following as a single logarithm:
Using the rule , the expression can be written as
Then, using the rule , this expression can be written as
Finally, using , we can write it as
This simplifies to
Example 2 – Expand the following in terms of logs of x, y and z:
Using the rules for adding and subtracting logs with the same base, we can expand the expression as follows:
Using the rule for dealing with powers inside the log, this becomes:
Note that , hence the half in the final expression.
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