\Log"a*rithm\ (l[o^]g"[.a]*r[i^][th]'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.
Note: 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, 0 1 2 3 4
      Indices or logarithms 1 10 100 1000 10,000 Numbers in
      geometrical progression 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 10^{2} = 100, and 3 is the logarithm of 1,000,
      because 10^{3} = 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}