In this chapter we show several ways of introducing logarithmic functions. Napier (1550–1617) invented logarithms originally as an aid to computation, by a method similar to the one we use in section 2.5. Later on, Briggs showed that logarithms to base 10 are more suitable for practical computation. Commercial slide rules exhibit a concrete model of logarithms to base 10. Since the advent of the computer and the hand calculator, logarithms and slide rules are no longer important for purposes of computing, but the logarithmic function is still fundamental for most branches of mathematics and many of its applications.

In sections 2.1-2.3 we give several ways of introducing the logarithmic function in connection with applications. The study of measuring information leads naturally to logarithms to base 2. We focus attention on the basic properties of this function, and especially on how to calculate it using only simple mathematics. This should remove most of the mystery that surrounds the numbers in logarithmic tables in the eyes of most students. The usual texts have an adequate supply of routine problems with which the teacher may supplement the material given here.

Another purpose of sections 2.1-2.3 is to show how a body of knowledge can be organized in the form of a deductive science. We try to give some idea of where postulates come from and how they are related to the real world. The insights of these sections should also be valuable in the teaching of high school geometry.

Sections 2.4 and 2.5 illustrate how the logarithmic function can be introduced at a more basic level.