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The Natural Logarithm

The inverse of the exponential function x = ey is the natural logarithm junction, written

y = ln x.

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

eln a = a,     ln(ea) = 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.

02_differentiation-305.gif

Figure 2.5.8


Last Update: 2006-11-25