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4.4 – Properties of Logarithms. 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.
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4.4 – Properties of Logarithms Objective: Students will be able to use properties to simplify logarithmic expressions.
Simplify • 1. (26)(28) • 2. (3–2)(35) • 3. • 4.
Product Property of Logarithms • Remember that to multiply powers with the same base, you add exponents.
This property also works backwards… Helpful Hint Think: logj+ loga+ logm = logjam
Example 1 • Directions: Express each logarithm as a single logarithm. Then simplify if possible. • log64 + log69
Example 2 • log5625 + log525
Example 3… your turn • log27 + log
Caution Just as a5b3 cannot be simplified, logarithms must have the same base to be simplified. Quotient Property of Logarithms • Remember that to divide powers with the same base, you subtract exponents
Example 4 • Directions: Express each logarithm as a single logarithm. Simplify, if possible. • log5100 – log554
Example 5 • log749 – log77
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. log2326 B. log8420
Example 7 • Express as a product. Simplify, if possible. • a. log104 b. log5252
Homework for tonight • Homework # _____ • Textbook pg. 260 # 20, 21, 23, 24, 26, 27, 28, 31