Chapter 4: Logarithmic Functions

In the previous chapter, we began to examine exponential functions, such as, f(x) = 2^x.  We saw that, for most inputs, they are very difficult to computer without the aid of a calculator.  However, we saw that they are used to create mathematical models in a wide variety of applications, from banking and finance to medicine and geology.  This means that we will need to be able to solve equations involving exponential functions.  As we have seen, this means that we must understand how the inverses of an exponential functions behave, as well.  

Thus, in this chapter, we will examine the inverses of exponential functions.  Such functions are known as "logarithms".  While exponential functions were somewhat challenging, their notation was familiar and we could feel secure that they satisfied all the rules of exponents that we had learned before.  Logarithmic functions are even more challenging for most students for two reasons:

• The traditional notation associated with logarithmic functions may be confusing at first, since it is even somewhat different than the functional notation we have used so far.
• In addition, as with exponential functions, we must treat such functions as black-boxes.  

While we will learn to manipulate logarithms algebraically, just as we did for exponential functions, the algebraic rules that logarithms behave do not have the familiar look rules of exponents.  So will take some time to introduce the notation associated with logarithms, examine their properties in detail, and learn how to use them to solve equations involving exponentials.

Go to Introduction to Logarithms

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