Log"a*rithm (l&obreve;g"&adot;*r&ibreve;&thlig;'m), n. [Gr. lo`gos word, account, proportion +
'ariqmo`s number: cf.
F. logarithme.] (Math.) One of a class of auxiliary numbers, devised by John Napier, of Merchiston, Scotland
(1550-1617), to abridge arithmetical calculations, by the use of addition and subtraction in place of multiplication and division. The relation of logarithms to common numbers is that of numbers in an
arithmetical series
to corresponding numbers in a
geometrical series, so that sums and differences of the former
indicate respectively products and
quotients of the latter; thus,
Hence, the logarithm of any given number is the
exponent of a power to which another given invariable number, called the base, must be raised in
order to produce that given number. Thus, let 10 be
the base, then 2 is the
logarithm of 100, because 102 = 100, and 3 is the logarithm of 1,000, because 103 = 1,000. Arithmetical complement of a logarithm, the difference between a logarithm and the number ten. -- Binary
logarithms. See under
Binary. -- Common logarithms, or
Brigg's logarithms, logarithms of which the
base is 10; -- so called from Henry Briggs, who invented
them. -- Gauss's logarithms, tables of
logarithms constructed for facilitating the operation of finding the logarithm of the sum of difference of two quantities from the logarithms of the quantities, one entry of
those tables and two additions or subtractions
answering the purpose of three entries of the common
tables and one addition or subtraction. They were suggested by the celebrated German mathematician
Karl Friedrich Gauss (died in 1855), and are of great
service in many astronomical
computations. -- Hyperbolic, or Napierian,
logarithms, those logarithms (devised by John Speidell, 1619) of which the
base is 2.7182818; -- so called from Napier, the inventor of logarithms. -- Logistic or
Proportionallogarithms., See under Logistic.
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