CHAPTER 4 - Exponential and Logarithmic Functions

Abstract

This chapter focuses on on the exponential and logarithmic functions. Functions of the form f(x) = ax are called exponential functions. The variable x appears as an exponent on some base a. However, the base a must be positive (a > 0) and not equal to one (a ≠ 1). A function f(x) = ax is increasing if a > 1 and decreasing if 0 < a <1. Another function f(x) = a−x is decreasing if a > 1 and decreasing if 0 <a <1. If ax = ay, then x = y, and if ax = bx, then a = b. The logarithmic function y = log ax is the inverse of the exponential function y = ax. The base a of the logarithmic function is restricted: a > 0 and a ≠ 1. This is exactly the same restriction that the base a has in the exponential function y = ax. The logarithmic function y = log ax and y = ax suggests that if a is raised to the power y, the final output will be x.