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Logarithmic Functions

Introduction and Summary

Table of Contents

Terms

Like many types of functions, the exponential function has an inverse. This inverse is called the logarithmic function, and it is the focus of this chapter.

The first section explains the meaning of the logarithmic function f (x) = c·loga(x - h) + k . It describes how to evaluate logarithms and how to graph logarithmic functions. This section also addresses the domain and range of a logarithmic function, which are inverses of those of its corresponding exponential function.

The next section presents two special logarithmic functions--the common logarithmic function and the natural logarithmic function. The common logarithm is log10 x , and it corresponds to the "log" button on most calculators. The natural logarithm is loge x , and it corresponds to the "ln" button on most calculators. The natural log has a particular use in economics--it is used to perform calculations involving compound interest. This section addresses these calculations.

Section three deals with the properties of logarithms. The eight properties discussed in this section are helpful in evaluating logarithmic expressions by hand or using a calculator. They are also useful in simplifying and solving equations containing logarithms or exponents, which is the focus of the final section.

Logarithmic functions are important largely because of their relationship to exponential functions. Logarithms can be used to solve exponential equations and to explore the properties of exponential functions. They will also become extremely valuable in calculus, where they will be used to calculate the slope of certain functions and the area bounded by certain curves. In addition, they have practical applications in economics, such as those discussed in section two.

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