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Natural logarithm function

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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
is considered the “natural” base since we have
e  x
is the eigenfunction of the derivative, i.e.
In some scientific or engineering contexts, the notation
log x
may signify the common logarithm
log10 x
, in which case the natural logarithm is denoted
ln x


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).