Graph of log2x as a function of a positive real number x
In mathematics, the binary logarithm (log2n) 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.
its very simple derivative. The binarylogarithm uses base 2 and is frequently used in computer science. Logarithms were introduced by John Napier in...
remaining tree, the lookup performance is proportional to that of binarylogarithm. BSTs were devised in the 1960s for the problem of efficient storage...
mathematics, the common logarithm is the logarithm with base 10. It is also known as the decadic logarithm and as the decimal logarithm, named after its base...
can be used to denote the common (base 10) logarithm. It may also refer to the binary (base 2) logarithm in the context of computer science, particularly...
indicate the binary iterated logarithm, which iterates the binarylogarithm (with base 2 {\displaystyle 2} ) instead of the natural logarithm (with base...
this equals the binarylogarithm, but it differs from the logarithm for other numbers and it gives 2-adic order rather than the logarithm. Michael Stifel...
is taken to be 0. The logarithms in this formula are usually taken (as shown in the graph) to the base 2. See binarylogarithm. When p = 1 2 {\displaystyle...
0.301\,029\,995\,663\,981\,195.} The inverse of this number is the binarylogarithm of 10: log 2 10 = 1 log 10 2 ≈ 3.321 928 095 {\displaystyle \log...
or equal to the argument, and log 2 {\textstyle \log _{2}} is the binarylogarithm. This is because the worst case is reached when the search reaches...
– binarylogarithm (log2). (Also written as lb.) lsc – lower semi-continuity. lerp – linear interpolation. lg – common logarithm (log10) or binary logarithm...
{\displaystyle x} to an integer as a way to compute an approximation of the binarylogarithm log 2 ( x ) {\textstyle \log _{2}(x)} Use this approximation to compute...
binarylogarithm. Other units include the nat, which is based on the natural logarithm, and the decimal digit, which is based on the common logarithm...
Here ordr(n) is the multiplicative order of n modulo r, log2 is the binarylogarithm, and φ ( r ) {\displaystyle \varphi (r)} is Euler's totient function...
logarithm logb a is a number x such that bx = a. Analogously, in any group G, powers bk can be defined for all integers k, and the discrete logarithm...
information is the bit, or more correctly the shannon, based on the binarylogarithm. Although "bit" is more frequently used in place of "shannon", its...
the algorithm. When a fast computation for the integer part of the binarylogarithm or for the bit-length is available (like e.g. std::bit_width in C++20)...
been developed, by Srinivasa Ramanujan, Bill Gosper, and others. The binarylogarithm of the factorial, used to analyze comparison sorting, can be very accurately...
functions. Logarithms: the inverses of exponential functions; useful to solve equations involving exponentials. Natural logarithm Common logarithmBinary logarithm...
_{i=1}^{n}p(x_{i})\log p(x_{i}),} where the base of the logarithm determines the units (for example, the binarylogarithm corresponds to bits). In the case of transmitted...
the inverse of the natural logarithm – the exponential function. Thus, although the observed dependent variable in binary logistic regression is a 0-or-1...
photography, the dynamic range is often measured in "stops", which is the binarylogarithm of the ratio of highest and lowest distinguishable exposures; in an...
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