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e is a number that can be defined in many ways. First,
e = 1+ |
Also, e is the number such that
= 1 |
The numerical value of e is approximately 2.71828.... The function f (x) = e ^{x} is an exponential function, which is a function of the form f (x) = a ^{x} , where a is a positive constant. The graph of f (x) = e ^{x} is shown below.
The inverse of the function e ^{x} is the natural log function ln(x) . These two graphs are pictured below:
Recall that if log _{a} b = x , then x is the power that a must be raised to in order to equal b .
With the natural log, the base is e . So, for example, ln(e) = 1 . Because e ^{x} and ln(x) are inverses, the following relations hold:
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