Chapter 6: Exponential and Logarithmic Functions

Of all of the functions we study in this text, exponential and logarithmic functions are possibly the ones which impact everyday life the most. This section introduces us to these functions while the rest of the chapter will more thoroughly explore their properties. Up to this point, we have dealt with functions which involve terms like $x^2$ or $x^{2/3}$, in other words, terms of the form $x^p$ where the base of the term, $x$, varies but the exponent of each term, $p$, remains constant. In this chapter, we study functions of the form $f(x)=b^x$ where the base $b$ is a constant and the exponent $x$ is the variable. We start our exploration of these functions with $f(x)=2^x$. (Apparently this is a tradition. Every College Algebra book we have ever read starts with $f(x)=2^x$.) We make a table of values, plot the points and connect the dots in a pleasing fashion.