MAT 171 Precalculus Algebra T rigsted - 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

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 Objectives

Properties of Logarithms If b > 0, b ≠ 1, u and v represent positive numbers, and r is any real number, then Product rule: Quotient rule: Power rule:

Use the product rule for logarithms to expand each expression. Assume x > 0. Use the quotient rule for logarithms to expand each expression. Assume x > 0.

Use the power rule for logarithms to expand each expression. Assume x > 0.

Use the properties for logarithms to expand each expression. Assume x > 0.

Use the properties for logarithms to condense 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

Change of Base Formula For any positive base b ≠ 1 and for any positive real number u, then where a is any positive number such that a ≠ 1.

Use the Change of Base Formula to solve.