4.4 – Properties of Logarithms

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

Simplify1. (26)(28)

2. (3–2)(35)

3.

4.

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

This property also works backwards…

Think: logj + loga + logm = logjam

Helpful Hint

Example 1Directions: Express each logarithm as a single logarithm.

Then simplify if possible.

log64 + log

69

Example 2log

5625 + log

525

Example 3… your turnlog

27 + log

Quotient Property of LogarithmsRemember that to divide

powers with the same base, you subtract exponents

Just as a5b3 cannot be simplified, logarithms must have the same base to be simplified.

Caution

Example 4Directions: Express each logarithm as a single logarithm.

Simplify, if possible.

log5100 – log554

Example 5log

749 – log77

Power Property of LogarithmsBecause you can multiply logarithms, you can also take

powers of logarithms.

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

2326 B. log

8420

Example 7Express as a product. Simplify, if possible. a. log104 b. log

5252

Homework for tonightHomework # _____

Textbook pg. 260 # 20, 21, 23, 24, 26, 27, 28, 31