Exponential and Logarithmic Functions Chapter 9 Exponential and Logarithmic Functions

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 Chapter 1 Outline

§ 9.5 Common Logarithms

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

Common Logarithm Common Logarithm Properties

Find Common Logarithms of Powers of 10 Common Logarithms of Nonnegative Powers of 10

Find Common Logarithms of Powers of 10 Common Logarithms of Negative Powers of 10

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.

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.