Question:
I am currently studying compounding interests. I have
came across natural logarithms or the exponential 2.7182818.... .Now I do
know that if ln x = y, 2.7182818^y=x but I have not yet understood what
is so special about this number or what exactly is this number.... I mean
why cannot we say that the e=2.6 or e 2.8? ;how has it been derived that
e=2.7182818?

Replies:
The value of "e" is based on the slope of a graph. Mathmeticians wanted a
function that had a slope at a point equal to the actual value of the
original function at that point. Such a function has to be exponential,
y=a^x for some base a. Each positive value of "a" yields a slope equal to
the function value multiplied by a constant. To get slope and value
perfectly equal, the base has to be 2.7182818.....

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