# Chapter 9-5 Chapter 9 Exponential and Logarithmic Functions Copyright 2015, 2011, 2007 Pearson Education, Inc. Chapter 9-1 1 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 9-3

3 Common Logarithm 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 log a x log10 x ( x 0) Copyright 2015, 2011, 2007 Pearson Education, Inc. Chapter 9-4 4

Common Logarithm Common Logarithm Properties 1. log xy log x log y x 2. log log x log y y n log x n log x 3. x log 10 x 4. log 10 x

5. x 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 log 1 log 100 0 log 10 log 101 1 2 log 100 log 10 2

log 1000 log 103 3 log 10,000 log 10 4 4 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 1 log 0.1 log log10 1 1

10 1 2 log 0.01 log log10 2 100 1 log 0.001 log log10 3 3 1000 1 log 0.0001 log log10 4 4 10,000 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. 1 5 10 log1 log 5 log10 0 log 5 1 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 y log x means x 10 y 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