Chapter 9 Exponential and Logarithmic Functions Copyright 2015

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

Chapter Sections 9. 1 – 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 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 9 -2 2

§ 9. 5 Common Logarithms Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 9 -

Common Logarithm A common logarithm is a logarithm with a base of 10. When the base of a logarithm is not indicated, we assume the base is 10. Thus Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 9 -4 4

Common Logarithm Properties 1. 2. 3. 4. 5. Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 9 -5 5

Find Common Logarithms of Powers of 10 Common Logarithms of Nonnegative Powers of 10 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 9 -6 6

Find Common Logarithms of Powers of 10 Common Logarithms of Negative Powers of 10 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 9 -7 7

Approximate Common Logarithms Suppose we wish to estimate the value of log 5. Since 5 is between 1 and 10, we can conclude that log 5 is between log 1 and log 10. Thus we can conclude that log 5 is a number between 0 and 1. Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 9 -8 8

Common Logarithm Definition of a Common Logarithm For all positive numbers x The common logarithm of a positive number x is the exponent to which the base 10 must be raised to obtain the number x. Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 9 -9 9