The Natural Logarithm

The inverse of the exponential function x = e^y is the natural logarithm junction, written

y = ln x.

Verbally, ln x is the number y such that e^y = x. Since y = ln x is the inverse function of x = e^y, we have

e^{ln a} = a,     ln(e^a) = a.

The simplest values of y = ln x are

ln(1/e) = -1,     ln(1) = 0,     ln e = 1.

Figure 2.5.8 shows the graph of y = ln x. It is defined only for x > 0.