Question 658621
The number {{{e}}} is an important mathematical {{{constant}}}, 
approximately equal to {{{2.71828}}}, that is the {{{base}}} of 
the {{{natural}}} logarithm ln.

{{{e}}}is important simply because it has all those nice properties 
you've been studying. Whenever you take the derivative of {{{e^x}}} 
(that's {{{e}}} to the {{{x}}}), you get {{{e^x}}} back again

 It's the only function on Earth that will do that (except things 
like {{{5* e^x}}} and variants like that). That's pretty cool stuff.

{{{Exponentially}}}{{{ changing}}} functions are written as {{{e^x}}}, 
where a represents the rate of the exponential change.

In such cases where exponential changes are involved we usually use 
another kind of logarithm called {{{natural}}}{{{ logarithm}}}. 

The {{{natural}}}{{{ logarithm}}} can be thought of as {{{Logarithm }}}{{{Base-e}}}. What this means is that it is a logarithmic operation 
that when carried out on {{{e}}} raised to {{{some}}}{{{ power}}} gives 
us the {{{power}}}{{{ itself}}}. 

This logarithm is labeled with ln (for "natural log") and its definition is: {{{ln(e^x) = x}}}.