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**logarithm**| logarithmetic | logarithmetical | logarithmetically | logarithmic | logarithmic scale

# logarithm

## 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,

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, because102 = 100 , and 3 is the logarithm of 1,000, because 103 = 1,000 ."
[

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

*1913 Webster*]**Arithmetical complement of a logarithm**,

**Binary logarithms**.

**Common logarithms**,

**Brigg's logarithms**

**Gauss's logarithms**,

**Hyperbolic logarithm**

**Napierian logarithm**

**Natural logarithm**

**Logistic logarithms**

**Proportional logarithms**

## 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

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