## logarithmThe logarithm of a number or variable x to base b, log_{b}
x, is the exponent of b
needed to give x. The bases most commonly used in mathematics are
e and 10. A logarithm to base e, written as log x
or ln x, is known as a natural logarithm. A logarithm
to base 10 is written as log_{10} x and is known as a common
logarithm. Since a^{0} = 1 for any a; log 1 = 0 for all bases.
In order to multiply two numbers together, one uses the fact that a
= ^{x}.a^{y}a^{x + y}, and hence log (x.y)
= log x + log y. We therefore look up the values of log
x and log y in logarithmic tables, add these values, and
then use the tables again to find the number whose logarithm is equal to
the result of the addition. Similarly, since a/^{x}a
= ^{y}a = log(^{x = y}x/y); and since (a)^{x}
= ^{y}a, log ^{xy}x = ^{y}y.log x.
Log_{x}x = 1 since x^{1} = x.
The antilogarithm of a number x is the number
whose logarithm is x; that is, if log y = x,
then y is the antilogarithm of x. A logarithmic curve is the plotting of a function
of the form f(x) = log x (i.e., a logarithmic
function). Logarithms, as an aid to calculation, were introduced by John Napier in 1614 and developed by Henry Briggs ## Related category• FUNCTIONS | |||||

Home • About • Copyright © The Worlds of David Darling • Encyclopedia of Alternative Energy • Contact |