= e x, where e is an irrational number whose decimal approximation to five
decimal places is 2.71828. We define e on Chapter 2.
E2. Logarithmic Functions
Since f(x) = ax is one-to-one, it has an inverse, f −1(x) = loga x, called the
logarithmic function with base a. We note that
y = loga x if and only if ay = x.The domain of logax is the set of positive reals; its range is the set of all reals. It
follows that the graphs of the pair of mutually inverse functions y = 2x and y =
log 2 x are symmetric to the line y = x, as can be seen in Figure N1–8.
Figure N1–8The logarithmic function loga x (a > 0, a ≠ 1) has the following properties:
The logarithmic base e is so important and convenient in calculus that we use
a special symbol:
logex = ln x.Logarithms with base e are called natural logarithms. The domain of ln x is the