The Number e
e is a number that can be defined in many ways. First,
|e = 1+|
Also, e is the number such that
The numerical value of e is approximately 2.71828.... The function f (x) = ex is an exponential function, which is a function of the form f (x) = ax, where a is a positive constant. The graph of f (x) = ex is shown below.
The Natural Log
The inverse of the function ex is the natural log function ln(x). These two graphs are pictured below:
Recall that if logab = 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 ex and ln(x) are inverses, the following relations hold: