3.3 Properties of Logarithms Students will rewrite logarithms with different bases. Students will use properties of logarithms to evaluate or rewrite logarithmic expressions. Students will use properties of logarithms to expand or condense logarithmic expressions. Students will use logarithmic functions to model and solve real-life problems.

Properties of Logarithms 1. If then

Example Solve

Change of Base Formula

Example 1 Change base using common log. a.b.

Example 2 Change base using natural log. a.b.

Example of

Example 3 Write each logarithm in terms of 2 and 3. a. b.

Example 4 Use the properties of logarithms to verify the statement:

Example 5 Use the properties of logarithms to expand each expression: a. b.

Example 6 Use the properties of logarithms to condense each logarithmic expression: a. b. c.