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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
, thus
Base
is considered the “natural” base since we have
where
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
.
Applications
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).