page 1 of 2

Page 1

Page 2

*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.

Figure %:Graph of the function *f* (*x*) = *e*^{x}

The inverse of the function *e*^{x} is the natural log function *ln*(*x*). These two graphs
are pictured below:

Figure %:*e*^{x} and *ln*(*x*) are inverses

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:

Page 1

Page 2

Take a Study Break!