Objective: Students will be able to use properties to simplify logarithmic expressions.

Simplify 1. (2 6 )(2 8 ) 2. (3 –2 )(3 5 ) 3. 4.

Product Property of Logarithms Remember that to multiply powers with the same base, you add exponents.

This property also works backwards… Think: log j + log a + log m = log jam Helpful Hint

Example 1 Directions: Express each logarithm as a single logarithm. Then simplify if possible. log log 6 9

Example 2 log log 5 25

Example 3… your turn log 27 + log

Quotient Property of Logarithms Remember that to divide powers with the same base, you subtract exponents Just as a 5 b 3 cannot be simplified, logarithms must have the same base to be simplified. Caution

Example 4 Directions: Express each logarithm as a single logarithm. Simplify, if possible. log – log 5 54

Example 5 log 7 49 – log 7 7

Power Property of Logarithms Because you can multiply logarithms, you can also take powers of logarithms.

Example 6 Express as a product. Simplify, if possible. A. log B. log

Example 7 Express as a product. Simplify, if possible. a. log10 4 b. log

Homework for tonight Homework # _____ Textbook pg. 260 # 20, 21, 23, 24, 26, 27, 28, 31