Section 6.5 - Properties of Logarithms
Section Objectives
- Apply the logarithm laws.
- Use the logarithm laws to expand logarithmic expressions.
- Use the logarithm laws to condense 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.