# E (Natural Log Definition)

## Colorized Definition

\newcommand{\growth}{\color{c1}}
\newcommand{\naturallog}{\color{c2}}
\newcommand{\unitInterest}{\color{c3}}
\newcommand{\timetogrow}{\color{c4}}
\newcommand{\unitTime}{\color{c5}}

$\displaystyle{ \naturallog \ln(a) \plain = \timetogrow \int _{1}^{a} \unitInterest {\frac {1}{x}} dx }$
$\displaystyle{ \naturallog \ln( \growth{e} \naturallog ) \plain = \unitTime 1 }$

\naturallog The natural log
\plain is
\timetogrow the time to grow from 1 to a value
\
\plain using
\unitInterest 100\% continuous interest.
\
\growth e is the number
\plain that takes
\naturallog the natural logarithm
\
\unitTime 1 unit of time to reach.

## Read More - [An Intuitive Guide To Exponential Functions & e](https://betterexplained.com/articles/an-intuitive-guide-to-exponential-functions-e/) - [Common Definitions of e (Colorized)](https://betterexplained.com/articles/definitions-of-e-colorized/) - [Demystifying the Natural Logarithm](https://betterexplained.com/articles/demystifying-the-natural-logarithm-ln/)