Definition of logarithm in US English:


(NZ log)


  • A quantity representing the power to which a fixed number (the base) must be raised to produce a given number.

    Logarithms can be used to simplify calculations because the addition and subtraction of logarithms is equivalent to multiplication and division, although the use of printed tables of logarithms for this has declined with the spread of electronic calculators. They also allow a geometric relationship to be represented conveniently by a straight line. The base of a common logarithm is 10, and that of a natural logarithm is the number e (2.71828…)

    • ‘Other topics to interest Carslaw throughout his career, which we have not touched on above, included an interest in non-euclidean geometry, Green's functions and the history of Napier's logarithms.’
    • ‘We can use arithmetics with different bases, fractions, decimals, logarithms, powers, or simply words.’
    • ‘Vega wrote on artillery but he is best remembered for his tables of logarithms and trigonometric functions.’
    • ‘It was a 17th century Scottish baron, John Napier, who first discovered the power of the logarithm as an important function in mathematics.’
    • ‘Initial assignment to linkage groups was based on the logarithm of the odds ratio for each possible marker pair.’
    • ‘The first tabulates logarithms of the sine, cosine, tangent and cotangent functions at 1 intervals and shows how to solve triangles using logarithmic functions.’
    • ‘All reading times were converted to words read per minute, then transformed to base 10 logarithms for the analyses because they were positively skewed.’
    • ‘They sketch a normalization algorithm, which is based on computing logarithms of transition matrices which they approximate by power series.’
    • ‘Prior to any statistical analysis, variables with non-normal distributions were transformed to logarithms, and percentage values were arcsin transformed.’
    • ‘The link between the harmonic series and logarithms is even more intimate.’
    • ‘He observed that the pages of heavily used books of logarithms were grimier at the beginning than at the end, suggesting that fellow scientists tended to look up smaller numbers more often than larger ones.’
    • ‘Other examples are negative numbers, complex numbers, trigonometry, raising to powers, logarithms, and the beginnings of calculus.’
    • ‘The tables of logarithms which he published included logarithms of trigonometric functions for use by astronomers.’
    • ‘The relationship between water potential and vapor pressure is well defined also, being proportional to the logarithm of the ratio of actual vapor pressure to the saturation vapor pressure.’
    • ‘The coefficients of this regression are the logarithm of the odds ratio.’
    • ‘The computation of logarithms had made him aware of the inaccuracy of human calculation around 1812.’
    • ‘The logarithm remains an important mathematical function but its use in calculating has gone for ever.’
    • ‘This was a person whose job was to perform long and arduous calculations to find the values of logarithms and trig functions, calculations we now perform with electronic calculators.’
    • ‘He invented logarithms independently of Napier using a totally different approach.’


Early 17th century: from modern Latin logarithmus, from Greek logos ‘reckoning, ratio’ + arithmos ‘number’.