The exponent or index of a number to a
specified base. If b^a = x, then a is the
logarithm of x to the base b. Before the
advent of cheap electronic calculators,
multiplication and division could be
simplified by being replaced with the
addition and subtraction of logarithms. For
any two numbers x and y (where x = b^a and y
= b^c) x x y = b^a x b^c = b^a + c; hence we
would add the logarithms of x and y, and look
up this answer in antilogarithm tables.
Tables of logarithms and antilogarithms are
available (usually to the base ten) that show
conversions of numbers into logarithms, and
vice versa. For example, to multiply 6,560 by
980, one looks up their logarithms - 3.8169
and 2.9912 - adds them together (6.8081),
then looks up the antilogarithm of this to
get the answer (6,428,800). Natural or
Napierian logarithms are to the base e, an
irrational number equal to approximately
2.7183. The principle of logarithms is also
the basis of the slide rule. With the general
availability of the electronic pocket
calculator, the need for logarithms has been
reduced. The first log tables (to base e)
were published by the Scottish mathematician
John Napier in 1614. Base-ten logs were
introduced by the Englishman Henry Briggs
(1561-1631) and Dutch mathematician Adriaen
Vlacq (1600-1667).