# What is e in Newton's Law of Cooling?

##### 1 Answer
Jan 10, 2016

$e$ is the base of the natural logarithm, that is, $\ln x = {\log}_{e} x$, where $e \approx 2.71828 \ldots$ is a very special number that occurs a lot in nature.

In mathematics, there are also other special ways to represent $e$ for example as the limit of a function

$e = {\lim}_{x \to 0} {\left(1 + x\right)}^{\frac{1}{x}} = {\lim}_{x \to \infty} {\left(1 + \frac{1}{x}\right)}^{x}$

or as the sum of an infinite power series

e^x=sum_(n=0)^oox^n/(n!)  and so e=sum_(n=0)^oo1/(n!).