Basic Logarithm Facts

Algebra: Logarithm Help


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What is e?

eq001

or, using summation notation:

eq002 where, for example, 5! = 5x4x3x2x1 and 0! = 1. My calculator carries the summation out to the 10th term.

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(xy) = (y)ln(x)

ln(xa/yb) = (a)ln(x) - (b)ln(y)

eln(x) = x


If xa = yb and we want to solve for x, we have:

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

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Algebra: Logarithm Help

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