Definify.com
Webster 1913 Edition
Logarithm
Log′a-rithm
(lŏg′ȧ-rĭth’m)
, Noun.
[Gr.
λόγοσ
word, account, proportion + ἀριθμόσ
number: cf. F. logarithme
.] (Math.)
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
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
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,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
10
, and 3 is the logarithm of 1,000, because 2
= 10010
. 3
= 1,000Arithmetical complement of a logarithm
, the difference between a logarithm and the number ten.
– Binary logarithms
. See under
– Binary
. Common logarithms
, or Brigg’s logarithms
logarithms of which the base is 10; – so called from
– Henry
, who invented them. Briggs
Gauss's logarithms
, tables of logarithms constructed for facilitating the operation of finding the logarithm of the sum of difference of two quantities from the logarithms of the quantities, one entry of those tables and two additions or subtractions answering the purpose of three entries of the common tables and one addition or subtraction. They were suggested by the celebrated German mathematician
– Karl Friedrich
(died in 1855), and are of great service in many astronomical computations. Gauss
Hyperbolic logarithm
or Napierian logarithm
or Natural logarithm
a logarithm (devised by John Speidell, 1619) of which the base is e (2.718281828459045...); – so called from , the inventor of logarithms.
– Napier
Logistic logarithms
or Proportional logarithms
See under
Logistic
.Webster 1828 Edition
Logarithm
LOG'ARITHM
,Noun.
Logarithms are the exponents of a series of powers and roots.
The logarithm of a number is that exponent of some other number, which renders the power of the latter, denoted by the exponent, equal to the former.
When the logarithms form a series in arithmetical progression, the corresponding natural numbers form a series in geometrical progression. Thus,
Logarithms 0 1 2 3 4 5
Natural numbers, 1 10 100 1000 10000 100000
The addition and subtraction of logarithms answer to the multiplication and division of their natural numbers. In like manner, involution is performed by multiplying the logarithm of any number by the number denoting the required power; and evolution, by dividing the logarithm by the number denoting the required root.
Logarithms are the invention of Baron Napier, lord of Marchiston in Scotland; but the kind now in use, were invented by Henry Briggs, professor of geometry in Gresham college at Oxford. They are extremely useful in abridging the labor of trigonometrical calculations.
Definition 2024
logarithm
logarithm
English
Noun
logarithm (plural logarithms)
- (mathematics) For a number , the power to which a given base number must be raised in order to obtain . Written . For example, because and because .
- For a currency which uses denominations of 1, 2, 5, 10, 20, 50, 100, 200, 500, 1000, etc., each jump in the base-10 logarithm from one denomination to the next higher is either 0.3010 or 0.3979.
Synonyms
Derived terms
- common logarithm
- natural logarithm
- log
- logarithmancy
- logarithmic
Translations
for a number x, the power to which a given base number must be raised in order to obtain x
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