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What is e?

or, using summation notation:

Rounding to 4 decimal places, e = 2.7183. e has a few nice properties, especially when it comes to calculus. It is the base of choice of real math wizards. The common notation for the log of x with base e is ln x.

ln(ab) = ln(a) + ln(b)

ln(a/b) = ln(a) - ln(b)

ln(x^y) = (y)ln(x)

ln(x^a/y^b) = (a)ln(x) - (b)ln(y)

e^ln(x) = x

(a)ln(x) = (b)ln(y)
ln(x) = (b/a)ln(y)
x = y^(b/a)