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What (who) is logarithmus dualis - definition
![[[Binary search]] in a sorted array, an algorithm whose time complexity involves binary logarithms](https://commons.wikimedia.org/wiki/Special:FilePath/Binary search into array - example.svg?width=200 "[[Binary search]] in a sorted array, an algorithm whose time complexity involves binary logarithms")
![[[HP-35]] [[scientific calculator]] (1972). The log and ln keys are in the top row; there is no log<sub>2</sub>{{hsp}}key.](https://commons.wikimedia.org/wiki/Special:FilePath/HP-35 Red Dot.jpg?width=200 "[[HP-35]] [[scientific calculator]] (1972). The log and ln keys are in the top row; there is no log<sub>2</sub>{{hsp}}key.")
![[[Leonhard Euler]] was the first to apply binary logarithms to [[music theory]], in 1739.](https://commons.wikimedia.org/wiki/Special:FilePath/Leonhard Euler - edit1.jpg?width=200 "[[Leonhard Euler]] was the first to apply binary logarithms to [[music theory]], in 1739.")
![A [[microarray]] for approximately 8700 genes. The expression rates of these genes are compared using binary logarithms.](https://commons.wikimedia.org/wiki/Special:FilePath/Mouse cdna microarray.jpg?width=200 "A [[microarray]] for approximately 8700 genes. The expression rates of these genes are compared using binary logarithms.")
![tournament bracket]] with the structure of a [[complete binary tree]]. The height of the tree (number of rounds of the tournament) is the binary logarithm of the number of players, rounded up to an integer.](https://commons.wikimedia.org/wiki/Special:FilePath/SixteenPlayerSingleEliminationTournamentBracket.svg?width=200 "tournament bracket]] with the structure of a [[complete binary tree]]. The height of the tree (number of rounds of the tournament) is the binary logarithm of the number of players, rounded up to an integer.")
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 Ti wagon (2015-07-03) 01 (cropped).jpg?width=200 "Nissan Dualis (facelift)")
 Ti wagon (2015-07-03) 02 (cropped).jpg?width=200 "Nissan Dualis (facelift)")
 – Heckansicht, 8. Juli 2012, Ratingen.jpg?width=200 "Nissan Qashqai+2 (facelift)")
 – Heckansicht, 24. August 2014, Düsseldorf.jpg?width=200 "Rear view")
.jpg?width=200 "2017 Nissan Qashqai (facelift)")
, front 10.10.20.jpg?width=200 "2020 Nissan Rogue Sport SV AWD (US; facelift)")
, rear 10.10.20.jpg?width=200 "2020 Nissan Rogue Sport SV AWD (US; facelift)")
 Auto Zuerich 2021 IMG 0487.jpg?width=200 "Interior")
Wikipedia
In mathematics, the binary logarithm (log2 n) is the power to which the number 2 must be raised to obtain the value n. That is, for any real number x,
For example, the binary logarithm of 1 is 0, the binary logarithm of 2 is 1, the binary logarithm of 4 is 2, and the binary logarithm of 32 is 5.
The binary logarithm is the logarithm to the base 2 and is the inverse function of the power of two function. As well as log2, an alternative notation for the binary logarithm is lb (the notation preferred by ISO 31-11 and ISO 80000-2).
Historically, the first application of binary logarithms was in music theory, by Leonhard Euler: the binary logarithm of a frequency ratio of two musical tones gives the number of octaves by which the tones differ. Binary logarithms can be used to calculate the length of the representation of a number in the binary numeral system, or the number of bits needed to encode a message in information theory. In computer science, they count the number of steps needed for binary search and related algorithms. Other areas in which the binary logarithm is frequently used include combinatorics, bioinformatics, the design of sports tournaments, and photography.
Binary logarithms are included in the standard C mathematical functions and other mathematical software packages. The integer part of a binary logarithm can be found using the find first set operation on an integer value, or by looking up the exponent of a floating point value. The fractional part of the logarithm can be calculated efficiently.
