8.5 Properties of Logarithms 3/21/2014

Properties of Logarithms Let m and n be positive numbers and b ≠ 1, Product Property Quotient Property Power Property

Expand and Condense Logarithmic Expressions Expand: is a sum and/or difference of logs. Condense: A single log expression.

Example 2 Expand a Logarithmic Expression Expand the expression. Assume all variables are positive. a. log 4 5x 2 log 7 y 3x3x b. SOLUTION a. log 4 5x 2 = log 4 5 log 4 x 2 + Product property = log log 4 x + Power property log 7 y 3x3x b. = log 7 3x log 7 y – Quotient property = log 7 3 log 7 x log 7 y – Product property +

Checkpoint Expand and Condense Logarithmic Expressions Expand the expression. Assume all variables are positive. 5. log 2 5x 6. log 2x 3 ANSWER log log x ANSWER log log 2 x 7. log 3 7 5x5x ANSWER log 3 5 – + log 3 xlog log 6 y 4x 24x 2 ANSWER log 6 4 – + 2 log 6 xlog 6 y

Example 3 Condense a Logarithmic Expression Condense the expression. a. log 16 2 log 2 – SOLUTION a. log 16 2 log 2 – = log 16 log 2 2 – Power property = log 2 16 Quotient property = log 4 Simplify.

Example 3 Condense a Logarithmic Expression 3 log 5 log 4 + = Power property log 5 3 log 4 + Product property = () log Simplify. = log log 5 log 4 b. + SOLUTION

Checkpoint Condense the expression. Assume all variables are positive. ANSWER log 5 3 ANSWER log 2 35 ANSWER log log 5 12log 5 4 – 10. log 2 7log log 42log log xlog y – ANSWER log y x 3x 3 Expand and Condense Logarithmic Expressions

Homework: 8.5 p.445 #34-56even