4 minutes Warm-Up Write each expression as a single logarithm. Then simplify, if possible. 1) log6 6 + log6 30 – log6 5 2) log6 5x + 3(log6 x – log6.

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4 minutes Warm-Up Write each expression as a single logarithm. Then simplify, if possible. 1) log6 6 + log6 30 – log6 5 2) log6 5x + 3(log6 x – log6 y)

10.3 Properties of Logarithmic Functions Objectives: Simplify and evaluate expressions involving logarithms Solve equations involving logarithms

Properties of Logarithms For b > 0 and b  1: Exponential-Logarithmic Inverse Property logb bx = x and b logbx = x for x > 0

Example 1 Evaluate each expression. a) b)

Practice Evaluate each expression. 1) 7log711 – log3 81

Properties of Logarithms For b > 0 and b  1: One-to-One Property of Logarithms If logb x = logb y, then x = y

Example 2 Solve log2(2x2 + 8x – 11) = log2(2x + 9) for x. 2x2 + 8x – 11 = 2x + 9 2x2 + 6x – 20 = 0 2(x2 + 3x – 10) = 0 2(x – 2)(x + 5) = 0 x = -5,2 Check: log2(2x2 + 8x – 11) = log2(2x + 9) log2 (–1) = log2 (-1) undefined log2 13 = log2 13 true

Practice Solve for x. 1) log5 (3x2 – 1) = log5 2x 2) logb (x2 – 2) + 2 logb 6 = logb 6x