List of logarithmic identities
In mathematics, many logarithmic identities exist. The following is a compilation of the notable of these, many of which are used for computational purposes.
Logarithmic growth
In mathematics, logarithmic growth describes a phenomenon whose size or cost can be described as a logarithm function of some input. e.g. y = C log (x). Note that any logarithm base can be used, since
History of logarithms
The history of logarithms is the story of a correspondence (in modern terms, a group isomorphism) between multiplication on the positive real numbers and addition on the real number line that was form
Index of logarithm articles
This is a list of logarithm topics, by Wikipedia page. See also the list of exponential topics.
* Acoustic power
* Antilogarithm
* Apparent magnitude
* Baker's theorem
* Bel
* Benford's law
* B
Logarithmic Sobolev inequalities
In mathematics, logarithmic Sobolev inequalities are a class of inequalities involving the norm of a function f, its logarithm, and its gradient . These inequalities were discovered and named by Leona
Napierian logarithm
The term Napierian logarithm or Naperian logarithm, named after John Napier, is often used to mean the natural logarithm. Napier did not introduce this natural logarithmic function, although it is nam
LogSumExp
The LogSumExp (LSE) (also called RealSoftMax or multivariable softplus) function is a smooth maximum – a smooth approximation to the maximum function, mainly used by machine learning algorithms. It is
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, sinc
Hyperbolic sector
A hyperbolic sector is a region of the Cartesian plane bounded by a hyperbola and two rays from the origin to it. For example, the two points (a, 1/a) and (b, 1/b) on the rectangular hyperbola xy = 1,
Logarithmic decrement
Logarithmic decrement, , is used to find the damping ratio of an underdamped system in the time domain. The method of logarithmic decrement becomes less and less precise as the damping ratio increases
Log semiring
In mathematics, in the field of tropical analysis, the log semiring is the semiring structure on the logarithmic scale, obtained by considering the extended real numbers as logarithms. That is, the op
Discrete logarithm records
Discrete logarithm records are the best results achieved to date in solving the discrete logarithm problem, which is the problem of finding solutions x to the equation given elements g and h of a fini
List of representations of e
The mathematical constant e can be represented in a variety of ways as a real number. Since e is an irrational number (see proof that e is irrational), it cannot be represented as the quotient of two
Smearing retransformation
The Smearing retransformation is used in regression analysis, after estimating the logarithm of a variable. Estimating the logarithm of a variable instead of the variable itself is a common technique
Super-logarithm
In mathematics, the super-logarithm is one of the two inverse functions of tetration. Just as exponentiation has two inverse functions, roots and logarithms, tetration has two inverse functions, super
Logarithmic convolution
In mathematics, the scale convolution of two functions and , also known as their logarithmic convolution is defined as the function when this quantity exists.
Alphonse Antonio de Sarasa
Alphonse Antonio de Sarasa was a Jesuit mathematician who contributed to the understanding of logarithms, particularly as areas under a hyperbola. Alphonse de Sarasa was born in 1618, in Nieuwpoort in
Logarithm of a matrix
In mathematics, a logarithm of a matrix is another matrix such that the matrix exponential of the latter matrix equals the original matrix. It is thus a generalization of the scalar logarithm and in s
Logarithmic mean
In mathematics, the logarithmic mean is a function of two non-negative numbers which is equal to their difference divided by the logarithm of their quotient. This calculation is applicable in engineer
Natural logarithm of 2
The decimal value of the natural logarithm of 2 (sequence in the OEIS)is approximately The logarithm of 2 in other bases is obtained with the formula The common logarithm in particular is (OEIS: ) The
Logarithmic spiral
A logarithmic spiral, equiangular spiral, or growth spiral is a self-similar spiral curve that often appears in nature. The first to describe a logarithmic spiral was Albrecht Dürer (1525) who called
Mirifici Logarithmorum Canonis Descriptio
Mirifici Logarithmorum Canonis Descriptio (Description of the Wonderful Canon of Logarithms, 1614) and Mirifici Logarithmorum Canonis Constructio (Construction of the Wonderful Canon of Logarithms, 16
Complex logarithm
In mathematics, a complex logarithm is a generalization of the natural logarithm to nonzero complex numbers. The term refers to one of the following, which are strongly related:
* A complex logarithm
Logarithmic differentiation
In calculus, logarithmic differentiation or differentiation by taking logarithms is a method used to differentiate functions by employing the logarithmic derivative of a function f, The technique is o
Iterated logarithm
In computer science, the iterated logarithm of , written (usually read "log star"), is the number of times the logarithm function must be iteratively applied before the result is less than or equal to
Logarithmic number system
A logarithmic number system (LNS) is an arithmetic system used for representing real numbers in computer and digital hardware, especially for digital signal processing.
Logarithmic distribution
In probability and statistics, the logarithmic distribution (also known as the logarithmic series distribution or the log-series distribution) is a discrete probability distribution derived from the M
Pollard's kangaroo algorithm
In computational number theory and computational algebra, Pollard's kangaroo algorithm (also Pollard's lambda algorithm, see below) is an algorithm for solving the discrete logarithm problem. The algo
Discrete logarithm
In mathematics, for given real numbers a and b, the 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 logarith
Transseries
In mathematics, the field of logarithmic-exponential transseries is a non-Archimedean ordered differential field which extends comparability of asymptotic growth rates of elementary nontrigonometric f
Otis King
Otis Carter Formby King (1876–1944) was an electrical engineer in London who invented and produced a cylindrical slide rule with helical scales, primarily for business uses initially. The product was
Log probability
In probability theory and computer science, a log probability is simply a logarithm of a probability. The use of log probabilities means representing probabilities on a logarithmic scale, instead of t
Mercator series
In mathematics, the Mercator series or Newton–Mercator series is the Taylor series for the natural logarithm: In summation notation, The series converges to the natural logarithm (shifted by 1) whenev
Slide rule scale
A slide rule scale is a line with graduated markings inscribed along the length of a slide rule used for mathematical calculations. The earliest such device had a single logarithmic scale for performi
Bygrave slide rule
The Bygrave slide rule is a slide rule named for its inventor, Captain Leonard Charles Bygrave of the RAF. It was used in celestial navigation, primarily in aviation. Officially, it was called the A.
Slide rule
The slide rule is a mechanical analog computer which is used primarily for multiplication and division, and for functions such as exponents, roots, logarithms, and trigonometry. It is not typically de
Pollard's rho algorithm for logarithms
Pollard's rho algorithm for logarithms is an algorithm introduced by John Pollard in 1978 to solve the discrete logarithm problem, analogous to Pollard's rho algorithm to solve the integer factorizati
Prime number theorem
In mathematics, the prime number theorem (PNT) describes the asymptotic distribution of the prime numbers among the positive integers. It formalizes the intuitive idea that primes become less common a
Natural logarithm
The natural logarithm of a number is its logarithm to the base of the mathematical constant e, which is an irrational and transcendental number approximately equal to 2.718281828459. The natural logar
Binary logarithm
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
Grégoire de Saint-Vincent
Grégoire de Saint-Vincent - in latin : Gregorius a Sancto Vincentio, in dutch : Gregorius van St-Vincent - (8 September 1584 Bruges – 5 June 1667 Ghent) was a Flemish Jesuit and mathematician. He is r
Gaussian logarithm
In mathematics, addition and subtraction logarithms or Gaussian logarithms can be utilized to find the logarithms of the sum and difference of a pair of values whose logarithms are known, without know
Logit
In statistics, the logit (/ˈloʊdʒɪt/ LOH-jit) function is the quantile function associated with the standard logistic distribution. It has many uses in data analysis and machine learning, especially i
Common logarithm
In 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, or Briggsian logarithm, after Henry Br