Definition of Logarethm
Logarithm, the exponent of the power to which a fixed number, called
the base, must be raised to produce a certain given number.
- Wikipedia
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,
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 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.
- Webster's Unabridged Dictionary (1913)
- (Mathematics) for a number x , the power to which a given number (called the base of the logarithm) must be raised in order to obtain x
- The Nuttall Encyclopedia
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