base (logarithms) The number whose powers are used as
logarithms. The most commonly used bases are 10, where if
y = log(
x),
x = 10
y; and e, the base of
natural logarithms, often written ln, so that if
y = ln(
x)
x = e
y. Logarithms to base 10 were originally popular: before the advent of electronic calculators they had to be looked up in numerical tables. Natural logarithms are nowadays more popular, since if
y = ln(
x), the rate of change of
y over time equals the proportional growth rate of
x, thus
dy/
dt = (
dx/
dt)/
x. Most calculators now have keys for both logs to base 10 and natural logarithms (ln) to base e.
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