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This definition gives rise to a function that coincides with the binary logarithm on the powers of two, [3] but it is different for other integers, giving the 2-adic order rather than the logarithm. [4] The modern form of a binary logarithm, applying to any number (not just powers of two) was considered explicitly by Leonhard Euler in 1739 ...
Binary logarithms are also used in computer science, where the binary system is ubiquitous; in music theory, where a pitch ratio of two (the octave) is ubiquitous and the number of cents between any two pitches is a scaled version of the binary logarithm, or log 2 times 1200, of the pitch ratio (that is, 100 cents per semitone in conventional ...
The complex logarithm is the complex number analogue of the logarithm function. No single valued function on the complex plane can satisfy the normal rules for logarithms. However, a multivalued function can be defined which satisfies most of the identities.
ld – binary logarithm (log 2). (Also written as lb.) lsc – lower semi-continuity. lerp – linear interpolation. [5] lg – common logarithm (log 10) or binary logarithm (log 2). LHS – left-hand side of an equation. Li – offset logarithmic integral function. li – logarithmic integral function or linearly independent.
A similar LNS named "signed logarithmic number system" (SLNS) was described in 1975 by Earl Swartzlander and Aristides Alexopoulos; rather than use two's complement notation for the logarithms, they offset them (scale the numbers being represented) to avoid negative logs. [3]
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 log 2, an alternative notation for the binary logarithm is lb (the notation ...
The logarithmic change-of-base formula, one of the logarithmic identities used frequently in algebra and calculus. The method for changing between polynomial and normal bases, and similar transformations, for purposes of coding theory and cryptography. Construction of the fiber product of schemes, in algebraic geometry.
The most common unit of information is the bit, or more correctly the shannon, [2] based on the binary logarithm. Although bit is more frequently used in place of shannon , its name is not distinguished from the bit as used in data processing to refer to a binary value or stream regardless of its entropy (information content).
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