Abstract
A function of the form f(x) = ax for a > 0 and a ≠ 1 is called an exponential function. When x is a rational number, the value of ax is defined in the usual way. If x is an irrational number, then ax is defined as the limit of ax, where xn is rational and approaches x. This chapter discusses the properties that exponential functions obey. The properties are immediate consequences of the definition when x1 and x2 are both rational. They are also valid when either x1 or x2 or both of x1 and x2 are irrational x. The properties of exponential functions are reflected in their graphs. The chapter also discusses logarithms and logarithmic functions. It lists several properties of the logarithmic function. These properties follow from the properties of the exponential function and are used in the calculation of the derivative of the logarithmic function.
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