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Possible Duplicate:
What's so “natural” about the base of natural logarithms?

Why the number e(=2.71828) was chosen as the natural base for logarithm functions ? Mainly I am interested in knowing why is it called "natural " . The number "2" could instead have been chosen as the most natural base.

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    I posted some reasons in the comments [here](http://math.stackexchange.com/questions/797/whats-so-natural-about-the-base-of-natural-logarithms).2014-12-09

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The simplest answer is this:

If you draw the graphs of $y=a^x$ for varying values of $a$, you find that they all pass through the point$(0,1)$ on the $y$-axis. There is exactly one of these curves that passes through that point with a gradient of exactly 1, and that value is obtained by taking $a=2.718281828459 \dots$.

In more analytical terms, this means that this is the value of $a$ which makes the derivative of $a^x$ equal to $a^x$, rather than a constant multiple of $a^x$.

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    @HenningMakholm: I still don't understand why it seems to you to be$a$disagreement? He quotes the statement (about the gradient of the exponential function being 1) and says "Not coincidentally, ... the exponential function... yields ... tangent line ... slope of 1". This is to provide evidence for the claim, not disagree with it. Anyway, the confusion seems cleared up now (I hope).2012-07-30