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

*‘proportional to the logarithm to the base 10 of the concentration’**‘We can use arithmetics with different bases, fractions, decimals, logarithms, powers, or simply words.’**‘Other examples are negative numbers, complex numbers, trigonometry, raising to powers, logarithms, and the beginnings of calculus.’**‘It was a 17th century Scottish baron, John Napier, who first discovered the power of the logarithm as an important function in mathematics.’**‘The first tabulates logarithms of the sine, cosine, tangent and cotangent functions at 1 intervals and shows how to solve triangles using logarithmic functions.’**‘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 logarithm remains an important mathematical function but its use in calculating has gone for ever.’**‘All reading times were converted to words read per minute, then transformed to base 10 logarithms for the analyses because they were positively skewed.’**‘Initial assignment to linkage groups was based on the logarithm of the odds ratio for each possible marker pair.’**‘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.’**‘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.’**‘The tables of logarithms which he published included logarithms of trigonometric functions for use by astronomers.’**‘The computation of logarithms had made him aware of the inaccuracy of human calculation around 1812.’**‘He invented logarithms independently of Napier using a totally different approach.’**‘The link between the harmonic series and logarithms is even more intimate.’**‘Vega wrote on artillery but he is best remembered for his tables of logarithms and trigonometric functions.’**‘The coefficients of this regression are the logarithm of the odds ratio.’**‘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.’**‘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.’*

Logarithms can be used to simplify calculations, as the addition and subtraction of logarithms is equivalent to multiplication and division, though 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 …)

**Origin**

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

**Pronunciation**

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