# Natural logarithm

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Natural 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.

### Look at other dictionaries:

• natural logarithm — Napierian logarithm, Napierian logarithms n. logarithm which has the irrational number e as its base (Mathematics) …   English contemporary dictionary

• natural logarithm — n. a logarithm to the base e …   English World dictionary

• Natural logarithm — Base e redirects here. For the numbering system which uses e as its base, see Non integer representation#Base e. Graph of the natural logarithm function. The function slowly grows to positive infinity as x increases and rapidly goes to negative… …   Wikipedia

• Natural logarithm of 2 — The decimal value of the natural logarithm of 2 (sequence A002162 in OEIS) is approximately as shown in the first line of the table below. The logarithm in other bases is obtained with the formula The common logarithm in particular is ( …   Wikipedia

• natural logarithm — noun The logarithm in base e; either the function that given returns such that or the value of . The natural logarithm can be used to integrate 1/x. Syn: hyperbolic logarithm, ln, natural log See Also: common logarithm, logarithm …   Wiktionary

• natural logarithm — natūrinis logaritmas statusas T sritis fizika atitikmenys: angl. Napierian logarithm; natural logarithm vok. natürlicher Logarithmus, m; Neperscher Logarithmus, m rus. натуральный логарифм, m pranc. logarithme naturel, m; logarithme népérien, m …   Fizikos terminų žodynas

• Natural logarithm — Logarithm to the base e (approximately 2.7183). The New York Times Financial Glossary …   Financial and business terms

• natural logarithm — Logarithm to the base e (approximately 2.7183). Bloomberg Financial Dictionary …   Financial and business terms

• natural logarithm — Math. a logarithm having e as a base. Symbol: ln Also called Napierian logarithm. Cf. common logarithm. [1810 20] * * * …   Universalium

• natural logarithm — nat′ural log′arithm n. math. a logarithm having e as a base Symbol: ln Also called Napierian logarithm Compare common logarithm …   From formal English to slang