# logarithm

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Related to logarithm: natural logarithm

## log·a·rithm

(lô′gə-rĭth′əm, lŏg′ə-)
n. Mathematics
The power to which a base, such as 10, must be raised to produce a given number. If nx = a, the logarithm of a, with n as the base, is x; symbolically, logn a = x. For example, 103 = 1,000; therefore, log10 1,000 = 3. The kinds most often used are the common logarithm (base 10), the natural logarithm (base e), and the binary logarithm (base 2).

[New Latin logarithmus : Greek logos, reason, proportion; see leg- in Indo-European roots + Greek arithmos, number; see ar- in Indo-European roots.]

log′a·rith′mic (-rĭth′mĭk), log′a·rith′mi·cal (-mĭ-kəl) adj.
log′a·rith′mi·cal·ly adv.

## logarithm

(ˈlɒɡəˌrɪðəm)
n
(Mathematics) the exponent indicating the power to which a fixed number, the base, must be raised to obtain a given number or variable. It is used esp to simplify multiplication and division: if ax = M, then the logarithm of M to the base a (written logaM) is x. Often shortened to: log See also common logarithm, natural logarithm
[C17: from New Latin logarithmus, coined 1614 by John Napier, from Greek logos ratio, reckoning + arithmos number]

## log•a•rithm

(ˈlɔ gəˌrɪð əm, -ˌrɪθ-, ˈlɒg ə-)

n.
the exponent of the power to which a base number must be raised to equal a given number; log: 2 is the logarithm of 100 to the base 10 (2 = log10 100).
[1605–15; < New Latin logarithmus < Greek log- log- + arithmós number; see arithmetic]

## log·a·rithm

(lô′gə-rĭth′əm)
The power to which a base must be raised to produce a given number. For example, if the base is 10, then 3 is the logarithm of 1,000 (written log 1,000 = 3) because 103 = 1,000.

## logarithm

- From Greek logos, "reckoning, ratio," and arithmos, "number."
See also related terms for reckoning.
ThesaurusAntonymsRelated WordsSynonymsLegend:
 Noun 1 logarithm - the exponent required to produce a given numberlogexponent, index, power - a mathematical notation indicating the number of times a quantity is multiplied by itselfcommon logarithm - a logarithm to the base 10Napierian logarithm, natural logarithm - a logarithm to the base e
Translations
لوغاريثْم
logaritmus
logaritme
logaritmi
logaritam
logaritmus
lógaritmi
logaritmas
logaritms
logaritmus
logaritm
ลอการิทึม

[ˈlɒgərɪθəm] N

## logarithm

[ˈlɒgərɪðəm] nlog book n
(formerly) (= registration document) [car] → carte grise
[traveller, explorer] → carnet m de route; [lorry driver] → carnet m de route
[movement of goods] → log cabin nlog fire n

nLogarithmus m

## logarithm

[ˈlɒgəˌrɪðm] nlogaritmo
common logarithm →

## logarithm

(ˈlogəriðəm) noun
(abbreviated to log (log) ) the number of times eg 10 must be multiplied by itself to produce a particular number. 10  10  10 or 103 = 1,000, so 3 is here the logarithm of 1,000.
References in classic literature ?
All human actions will then, of course, be tabulated according to these laws, mathematically, like tables of logarithms up to 108,000, and entered in an index; or, better still, there would be published certain edifying works of the nature of encyclopaedic lexicons, in which everything will be so clearly calculated and explained that there will be no more incidents or adventures in the world.
I, for instance, would not be in the least surprised if all of a sudden, a propos of nothing, in the midst of general prosperity a gentleman with an ignoble, or rather with a reactionary and ironical, countenance were to arise and, putting his arms akimbo, say to us all: "I say, gentleman, hadn't we better kick over the whole show and scatter rationalism to the winds, simply to send these logarithms to the devil, and to enable us to live once more at our own sweet foolish will
But it is best not to be intimate with gentlemen of this profession and to take the calculations at second hand, as you do logarithms, for to work them yourself, depend upon it, will cost you something considerable.
Introductory chapters cover basics of exponents and logarithms, algebraic techniques in exponent and logarithm problems, equations and systems of equations involving exponents and logarithms, and exponents and logarithms in number theory and in calculus.
Regression coefficients are estimated from the equation where endogenous variables and the volatility of the exchange rate are modeled using five exogenous variables: differentiation of position in the business cycle (expressed as the standard deviation of the difference in the logarithm of real output between country i and the Eurozone), dissimilarity of the export structure (sum of the absolute differences in the shares of chemical and manufacturing trade in total merchandise), intensity of the mutual trade links (mean of the ratio of bilateral exports to domestic GDP for countries i and j), size of the economy (mean of the logarithm of the two GDPs measured in euros) and openness of economies (mean of the shares of foreign trade turnover in GDP of country i and the Eurozone).
Improvement of PCRD algorithm based on logarithm function form
Interpreting a logarithm table to find an antilogarithm (Abelard, 2015) N 0 1 2 3 4 5 6 7 8 9 71 8513 8519 8525 8531 8537 8543 8549 8555 8561 8567 72 8573 8579 8579 8591 8597 8603 8609 8615 8621 8627 73 8633 8639 8639 8651 8657 8663 8669 8675 8681 8686 N Proportional parts 1 2 3 4 5 6 7 8 9 71 1 1 2 2 3 4 4 5 5 72 1 1 2 2 3 4 4 5 5 73 1 1 2 2 3 4 4 5 5
These were the number of major road lanes, the lane width of major roads, the logarithm of heavy vehicle volume turning left on major roads, the logarithm of total traffic volume driving straight on major roads, the logarithm of total traffic volume turning left on major roads, the logarithm of total traffic volume turning right on minor roads, the length of median barrier on major roads, the length of median barrier on minor roads, and the existence of a traffic island on major roads.
Natural logarithm of deposits is positively related to the total expenses of a bank for each year in the sample and the relationship is statistically significant in all years except for the years 2010 to 2013.
The results of the unit root test for first-order difference variables, except for that ofthe price index logarithm and trade liberalization logarithm, are shown in Table 2.
Economies of Scale are Measured on the Basis of Size as Measured by Assets Variables 2007 2008 2009 Number of Banks 13 13 13 Dependent Variable: Natural Logarithm of Total Expenses Adjusted R- 0.

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