CHAPTER 5 - EXPONENTIAL AND LOGARITHM FUNCTIONS

Abstract

This chapter presents the exponential and logarithm functions. The function f(x) = ax, where a is a positive number and x takes all real values is called the exponential function. The number a is called the base of the exponential function ax. The exponential function y = 10x is positive and increasing; y → ∞ as x → ∞ and y → 0 + as x → -∞. Hence, its graph crosses each horizontal line y = c, where c > 0, at exactly one point. If y >0, then there is one and only one real number x such that y = 10x. This number x is called the logarithm of y, and is written x = log y. The domain of logarithm function is the set of positive real numbers. The property of logarithm function states that each positive number has a logarithm, and each real number is the logarithm of a unique positive number. Logarithms are used to compute products, quotients, and powers.