The log-normal distribution

The log-normal distribution is simply the distribution of a set of values whose logarithm is normally distributed. The base of the logarithm can be any positive number except for one. Like the normal distribution, the log-normal distribution is important in the description of many naturally occurring phenomena.

A logarithm represents the power to which a fixed number (the base) must be raised to produce a given number. By plotting the logarithms as a histogram, we've shown that these powers are approximately normally distributed. Logarithms are usually taken to base 10 or base e: the transcendental number that's equal to approximately 2.718. Incanter's log function and its inverse exp both use base e. log_e is also called the natural logarithm or ln, because of the properties that make it particularly suitable in calculus.

The log-normal distribution tends to occur in processes of growth where the growth rate is independent of size. This is known as Gibrat's law...