The natural logarithm function
is the logarithm with base
, i.e. Euler’s number
. It is the inverse function of the [natural] exponential function
, also with base
is considered the “natural” base since we have
is the eigenfunction of the derivative, i.e.
In some scientific or engineering contexts, the notation
may signify the common logarithm
, in which case the natural logarithm is denoted
The natural log/e has ties to numerous applications, only a few of which include statistics (Poisson distribution), number theory (Prime number theorem), and thermodynamic (entropy).