Logarithm

Logarithm
Logarithm 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. [1913 Webster]

{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 logarithm} or {Napierian logarithm} or {Natural logarithm}, a logarithm (devised by John Speidell, 1619) of which the base is e (2.718281828459045...); -- so called from Napier, the inventor of logarithms.

{Logistic logarithms} or {Proportional logarithms}, See under {Logistic}. [1913 Webster]


The Collaborative International Dictionary of English. 2000.

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  • logarithm — 1610s, Mod.L. logarithmus, coined by Scottish mathematician John Napier (1550 1617), lit. ratio number, from Gk. logos proportion, ratio, word (see LOGOS (Cf. logos)) + arithmos number (see ARITHMETIC (Cf. arithmetic)) …   Etymology dictionary

  • logarithm — ► NOUN ▪ a quantity representing the power to which a fixed number (the base) must be raised to produce a given number. ORIGIN from Greek logos reckoning, ratio + arithmos number …   English terms dictionary

  • logarithm — [lôg′ə rith΄əm, läg′ə rithəm] n. [ModL logarithmus < Gr logos, a word, proportion, ratio (see LOGIC) + arithmos, number (see ARITHMETIC)] Math. the exponent expressing the power to which a fixed number (the base) must be raised in order to… …   English World dictionary

  • Logarithm — The graph of the logarithm to base 2 crosses the x axis (horizontal axis) at 1 and passes through the points with coordinates (2, 1), (4, 2), and (8, 3) …   Wikipedia

  • logarithm — /law geuh ridh euhm, rith , log euh /, n. Math. the exponent of the power to which a base number must be raised to equal a given number; log: 2 is the logarithm of 100 to the base 10 (2 = log10 100). [1605 15; < NL logarithmus < Gk lóg(os) LOG +… …   Universalium

  • logarithm — n. 1 one of a series of arithmetic exponents tabulated to simplify computation by making it possible to use addition and subtraction instead of multiplication and division. 2 the power to which a fixed number or base ({{}}see BASE(1) 7) must be… …   Useful english dictionary

  • logarithm — n. a common; natural logarithm * * * natural logarithm a common …   Combinatory dictionary

  • logarithm — UK [ˈlɒɡərɪð(ə)m] / US [ˈlɔɡəˌrɪðəm] noun [countable] Word forms logarithm : singular logarithm plural logarithms maths in mathematics, the number of times that a number must be multiplied by itself in order to produce a particular number …   English dictionary

  • logarithm — noun Etymology: New Latin logarithmus, from log + Greek arithmos number more at arithmetic Date: circa 1616 the exponent that indicates the power to which a base number is raised to produce a given number < the logarithm of 100 to the base 10 is… …   New Collegiate Dictionary

  • logarithm — [17] Greek lógos had a remarkably wide spread of meanings, ranging from ‘speech, saying’ to ‘reason, reckoning, calculation’, and ‘ratio’. The more ‘verbal’ end of its spectrum has given English the suffixes logue and logy (as in dialogue,… …   The Hutchinson dictionary of word origins

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