Abstract
This chapter discusses two of the most important functions of mathematics: the exponential and logarithmic functions. It discusses why they are important by giving a large variety of applications in physics, biology, and economics. There are two very different ways to define the exponential and logarithmic functions. The first of these starts with the basic rules of exponents and the second way starts off with a special integral. In both cases, one is led to the same functions. Both ways of defining these functions can give insight into how to work with them. It is useful to see how two very different approaches lead to the same central idea. The chapter discusses the relationship between the exponential and logarithmic functions and the differentiation and integration of more general exponential and logarithmic functions.
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