# 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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