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}
2. (Math.) Sexagesimal, or made on the scale of 60; as,
logistic, or sexagesimal, arithmetic.
{Logistic}, or {Proportional}, {logarithms}, certain
logarithmic numbers used to shorten the calculation of the
fourth term of a proportion of which one of the terms is a
given constant quantity, commonly one hour, while the
other terms are expressed in minutes and seconds; -- not
now used.