# Section 5.3 Properties of Logarithms

**Section Objectives**

- Apply the logarithm laws.
- Use the logarithm laws to expand logarithmic expressions.
- Use the logarithm laws to expand logarithmic expressions.
- Apply the change-of-base formula.

### Logarithm Laws

The following properties of logarithms are very useful.

**Warning:** Do not apply the logarithm laws when they do not apply. For example,

#### Examples

- Condense to a single logarithm:

- Condense to a single logarithm:

### Change-of-Base Formula

For any valid bases and and any positive real number ,

The change of base-of-base formula can be used to convert any log to a common or natural log.

- Compute by using the change-of-base formula.