Section 6.4 Properties of Logarithmic Functions Objectives:

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Presentation transcript:

Section 6.4 Properties of Logarithmic Functions Objectives: Simplify and evaluate expressions involving logarithms. Solve equations involving logarithms. Standard: 2.8.11.N. Solve equations.

am • an = am+n Product Property Product and Quotient Properties of Exponents am • an = am+n Product Property am/an = am-n Quotient Property (am)n = am*n Power Property

Product and Quotient Properties of Logarithms For m > 0, n > 0, b > 0, and b ≠ 1: Product Property logb (mn) = logb m + logb n Quotient Property logb (m/n) = logb m – logb n ** Just like the exponent rules!

A. log2 12 = log2 (2 ● 2 ● 3) = log2 2 + log2 2 + log2 3 ≈1 + 1 + 1.5850 ≈3.5850

B. log2 1.5 = log2 3/2 = log2 3 – log2 2 ≈1.5850 - 1 ≈0.5850

C. log 2 18 D. log2 .75

Write each expression as a single logarithm. Then simplify, if possible. A. log3 10 – log3 5 B. logb u + logb v – logb uw

C. log4 18 – log4 6 D. logb 4x - logb 3y + logb y

Power Property of Logarithms For m > 0, b > 0, b ≠ 1, and any real number p: logb mp = p logb m Ex 3. Evaluate log5 254 Log5 254 = 4 log5 25 = 4 ● 2 = 8

Power Property of Logarithms Ex 4. Evaluate log3 27100

Exponential- Logarithmic Inverse Properties: For b > 0, b ≠1: logb bx = x and blogbx = x for x > 0. A. 3log34 + log5 25 B. log2 32 – 5log53

C. 7log711 + log381 D. log885 +3log38

Homework Integrated Algebra II- Section 6.4 Level A Honors Algebra II- Section 6.4 Level B