logarithm

American  

[law-guh-rith-uhm, -rith-, log-uh-] / ˈlɔ gəˌrɪð əm, -ˌrɪθ-, ˈlɒg ə- /

noun

Mathematics.

1. 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).

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logarithm British  

/ ˈlɒɡəˌrɪðəm /

noun

1. Often shortened to: log.  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 log aM ) is x See also common logarithm natural logarithm

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logarithm Scientific  

/ lô′gə-rĭth′əm /

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

2. See more at common logarithm natural logarithm

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Etymology

Origin of logarithm

1605–15; < New Latin logarithmus < Greek lóg ( os ) log- + arithmós number; see arithmetic

Explanation

A logarithm is a mathematical concept involving multiplication. A logarithm is the exponent that will yield a certain number. For a base of 3 to produce 9, the logarithm would be 2. Every number has a logarithm that — if it were an exponent — would produce a certain number. For example, let's say the base is 5. The logarithm to produce 25 would be 2, because 5 times 5 is 25. If the base is 10, the logarithm to produce 10000 would be 4. The logarithm is also called the log. Scottish mathematician John Napier coined the word by using the Greek logos for "word or ratio” plus arithmos for "number.”

Example Sentences

Before calculators, people outsourced hairy arithmetic to reference books called logarithm tables.

From Scientific American • May 8, 2023

In 1881, astronomer Simon Newcomb noticed that early pages of logarithm tables, which correspond to numbers beginning with one, were grubby and worn compared with the pristine later pages.

From Scientific American • May 8, 2023

Note that this is a logarithm scale not a linear scale.

From Textbooks • Jun. 9, 2022

The logarithm of the number resulting from the division of two numbers is the difference between the logarithms of the two numbers.

From Textbooks • Feb. 14, 2019

The safety index associated with automobile driving is thus a relatively low 3.7, the logarithm of 5,300.

From "Innumeracy: Mathematical Illiteracy and Its Consequences" by John Allen Paulos