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171S5.4_p Properties of Logarithms MAT 171 Precalculus Algebra Trigsted Pilot Test Dr. Claude Moore Cape Fear Community College CHAPTER 5: Exponential and Logarithmic Functions and Equations 5.1 Exponential Functions 5.2 The Natural Exponential Function 5.3 Logarithmic Functions 5.4 Properties of Logarithms 5.5 Exponential and Logarithmic Equations 5.6 Applications of Exponential and Logarithmic Functions Properties of Logarithms April 14, 2011 Objectives 1. Using the Product Rule, Quotient Rule and Power Rule for Logarithms 2. Expanding and Condensing Logarithmic Expressions 3. Solving Logarithmic Equations Using the Logarithm Property of Equality 4. Using the Change of Base Formula Use the product rule for logarithms to expand each expression. Assume x > 0. If b > 0, b ≠ 1, u and v represent positive numbers, and r is any real number, then Product rule: Quotient rule: Use the quotient rule for logarithms to expand each expression. Assume x > 0. Power rule: 1 171S5.4_p Properties of Logarithms Use the power rule for logarithms to expand each expression. Assume x > 0. Use the properties for logarithms to condense each expression. Assume x > 0. April 14, 2011 Use the properties for logarithms to expand each expression. Assume x > 0. Logarithm Property of Equality If a logarithmic equation can be written in the form then u = v. Furthermore, if u = v, then Domain of log x is x > 0 x = -8 is an extraneous solution Solution is x = 8 2 171S5.4_p Properties of Logarithms Change of Base Formula April 14, 2011 Use the Change of Base Formula to solve. For any positive base b ≠ 1 and for any positive real number u, then where a is any positive number such that a ≠ 1. 3 171S5.4_p Properties of Logarithms April 14, 2011 4 171S5.4_p Properties of Logarithms April 14, 2011 5