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If a number, x, is expressed as a power of another number, y, that is, if x = yn, then n is said to be the logarithm of x to base y. Common logarithms are to the base 10; natural or Napierian logarithms are to the base e, a mathematical constant.
[G. logos, word, ratio, + arithmos, number]


a mathematical device.

common logarithm
the value of the power when a number is expressed as to the power of 10 (has the base 10). Thus 100 expressed as to the power of 10 is 102 and the log of 100 is 2.
Napierian logarithm
see natural logarithm (below).
natural logarithm
as for common logarithm, except that the base is e or 2.178. Called also Napierian logarithm.
References in periodicals archive ?
In 1938, physicist Frank Benford (1) observed that for a great number of interesting databases, the numbers are not arithmetically distributed but instead are logarithmically distributed.
In addition, the capacity grows logarithmically with the number of BS antennas Nr without bound.
68) (a) Intrameasurement procedure CV calculated from the SD of the logarithmically transformed results (SD,) of the 32 native individual samples ("S" in online Supplemental Table 1).
Crowd size was clearly the strongest predictor of HA; there was little or no HA for crowd sizes less than about 20,000, beyond which HA increased logarithmically to 66% at attendances of 80,000.
Multivariate analysis using General Linear Model (GLM) was performed with adjustments for gender, diabetes, age, BMI, equivalent dose and logarithmically transformed length of treatment.
This challenges the idea that mammalian brains perceive numbers logarithmically and may help researchers better understand how human beings process numbers.
where the loop integral is logarithmically UV divergent [varies] log(1/r) as the cut-off radius r [right arrow] 0.
The power of technology has increased logarithmically.
This realignment occurs again with cooling after assembly and the passage of time, so much so that its dielectric constant changes logarithmically.
In that case, using the value of 50 deaths per 100,000 person-years in 1983 and the value of about 2 in 2002 gives a suppression rate of more than 25-fold--"more than" because cancer incidence increases logarithmically with age, so the death rate should have increased with time, rather than decreasing.
For the first analysis, the indifference points of individual participants were fit using Equation 1, (4) and the resulting k values were then transformed logarithmically.