logarithm

• POS: Noun
• HYPHEN: log=a=rithm

CIDE DICTIONARY

logarithm, n. [Gr. lo`gos word, account, proportion + 'ariqmo`s number: cf. F. logarithme.].

 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."  [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.

OXFORD DICTIONARY

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 raised to produce a given number (the logarithm of 1000 to base 10 is 3).

Idiom

common logarithm a logarithm to the base 10. natural (or Napierian) logarithm a logarithm to the base e (2.71828.....).

Usage

Abbr.: ln or log**.

Derivative

logarithmic adj. logarithmically adv.

Etymology

mod.L logarithmus f. Gk logos reckoning, ratio + arithmos number

ROGET THESAURUS

logarithm

Number

N number, symbol, numeral, figure, cipher, digit, integer, counter, round number, formula, function, series, sum, difference, complement, subtrahend, product, multiplicand, multiplier, multiplicator, coefficient, multiple, dividend, divisor, factor, quotient, submultiple, fraction, rational number, surd, irrational number, transcendental number, mixed number, complex number, complex conjugate, numerator, denominator, decimal, circulating decimal, repetend, common measure, aliquot part, prime number, prime, relative prime, prime factor, prime pair, reciprocal, totient, binary number, octal number, hexadecimal number, permutation, combination, variation, election, ratio, proportion, comparison, progression, arithmetical progression, geometrical progression, harmonical progression, percentage, permilage, figurate numbers, pyramidal numbers, polygonal numbers, power, root, exponent, index, logarithm, antilogarithm, modulus, base, differential, integral, fluxion, fluent, numeral, complementary, divisible, aliquot, reciprocal, prime, relatively prime, fractional, decimal, figurate, incommensurable, proportional, exponential, logarithmic, logometric, differential, fluxional, integral, totitive, positive, negative, rational, irrational, surd, radical, real, complex, imaginary, finite, infinite, impossible, numerically, modulo.