1 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 9-1 Exponential and Logarithmic Functions Chapter 9

2 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter – Composite and Inverse Functions 9.2 – Exponential Functions 9.3 – Logarithmic Functions 9.4 – Properties of Logarithms 9.5 – Common Logarithms 9.6 – Exponential and Logarithmic Equations 9.7 – Natural Exponential and Natural Logarithmic Functions Chapter Sections

3 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 9-3 § 9.3 Logarithmic Functions

4 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 9-4 Define a Logarithm Logarithm For x > 0 and a > 0, a ≠ 1 The expression log a x is read “the logarithm of x to the base a” or simply “log, base a, of x.”

5 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 9-5 Convert from Exponential Form to Logarithmic Form To convert from an exponential equation to a logarithmic equation consider the following diagram: For example:

6 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 9-6 Exponential Functions Exponential FormLogarithmic Form 5 0 = 1log 10 1= = 8 log 2 8= 3

7 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 9-7 Graph Logarithmic Functions Logarithmic Function For any real number a > 0, a ≠ 1, and x > 0, is a logarithmic function. Examples of Logarithmic Functions

8 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 9-8 Graph Logarithmic Functions Graphs of Logarithmic Functions For all logarithmic functions of the form,where a > 0, a ≠ 1, and x > 0 1.The domain of the function is (0, ∞). 2.The range of the function is (-∞, ∞). 3.The graph passes through the points, (1, 0), and (a, 1).

9 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 9-9 Graph Logarithmic Functions Example Graph y = log 2 x. State the domain and range of the function. In this equation, y = log a x, where a = 2. y = log 2 x means x = 2 y. Using x = 2 y, construct a table of values. The domain, is {x|x > 0} and the range is (-∞, ∞).

10 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 9-10 Compare the Graphs of Exponential and Logarithmic Functions

11 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 9-11 Compare the Graphs of Exponential and Logarithmic Functions The graphs of y = ax and y = log a x for a > 1 are symmetric about the line y = x.