Logarithms and Exponentials
We expect that the reader has already met the logarithmic and exponential functions. The usual way to introduce the logarithmic function is to say that loga b = c, where b = ac. In Chapter 1, we defined ac only where c is rational. The most sensible way to define ac for general c is to use logarithms. We have a circular definition!
In this chapter, we give a definition of logarithm in terms of a definite integral. We establish the usual properties of log, including its derivative. It turns out that log : (0, ∞) → 
is bijective, and so has an inverse. This is the exponential function exp. Its properties are ...
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