Technical Mathematics, Sixth Edition

Chapter 18. Exponential and Logarithmic Functions

OBJECTIVES When you have completed this chapter, you should be able to Graph the exponential function. Solve exponential growth and decay problems by formula or by the universal growth and decay curves. Convert expressions between exponential and logarithmic form. Evaluate common and natural logarithms and antilogarithms. Evaluate, manipulate, and simplify logarithmic expressions. Solve exponential and logarithmic equations. Solve applied problems involving exponential or logarithmic equations.

According to legend, the inventor of chess asked that the reward for his invention be a single grain of wheat on the first square of a chessboard, then two grains on the second square, four on the next, and so forth, each square having double the number on the preceding square. If that were done, the total amount of wheat given would be greater than that grown by mankind since the beginning of agriculture. This is an illustration of the astounding properties of exponential growth.

We will study the exponential function here and give other, more practical examples of its use. We also introduce logarithms and study their properties. Logarithms were once widely used for computation but now have been replaced by calculators and computers. We will use logarithms mainly to solve exponential equations. Of course, we will also use our calculators to solve these equations, as well as the logarithmic equations to follow.

This chapter is loaded with interesting ...