logarithmˈlɔ gəˌrɪð əm, -ˌrɪθ-, ˈlɒg ə-
logarithm (n)
- plural
- logarithms
English Definitions:
logarithm, log (noun)
the exponent required to produce a given number
logarithm (Noun)
For a number , the power to which a given base number must be raised in order to obtain . Written . For example, because and because .
Logarithm
The logarithm of a number is the exponent to which another fixed value, the base, must be raised to produce that number. For example, the logarithm of 1000 to base 10 is 3, because 1000 is 10 to the power 3: 1000 = 10 × 10 × 10 = 10³. More generally, if x = b, then y is the logarithm of x to base b, and is written y = logb(x), so log10 = 3. The logarithm to base b = 10 is called the common logarithm and has many applications in science and engineering. The natural logarithm has the constant e as its base; its use is widespread in pure mathematics, especially calculus. The binary logarithm uses base b = 2 and is prominent in computer science. Logarithms were introduced by John Napier in the early 17th century as a means to simplify calculations. They were rapidly adopted by navigators, scientists, engineers, and others to perform computations more easily, using slide rules and logarithm tables. Tedious multi-digit multiplication steps can be replaced by table look-ups and simpler addition because of the fact—important in its own right—that the logarithm of a product is the sum of the logarithms of the factors: The present-day notion of logarithms comes from Leonhard Euler, who connected them to the exponential function in the 18th century.
Logarithm
In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a number x to the base b is the exponent to which b must be raised, to produce x. For example, since 1000 = 103, the logarithm base 10 of 1000 is 3, or log10 (1000) = 3. The logarithm of x to base b is denoted as logb (x), or without parentheses, logb x, or even without the explicit base, log x, when no confusion is possible, or when the base does not matter such as in big O notation. The logarithm base 10 is called the decimal or common logarithm and is commonly used in science and engineering. The natural logarithm has the number e ≈ 2.718 as its base; its use is widespread in mathematics and physics, because of its very simple derivative. The binary logarithm uses base 2 and is frequently used in computer science.
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"logarithm." Kamus.net. STANDS4 LLC, 2024. Web. 19 Apr. 2024. <https://www.kamus.net/english/logarithm>.
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