## Logarithm Wikipedia

### Logarithm - Wikipedia.

In mathematics, the logarithm is the inverse function to exponentiation.That means the logarithm of a given number x is the exponent to which another fixed number, the base b, must be raised, to produce that number x.In the simplest case, the logarithm counts the number of occurrences of the same factor in repeated multiplication; e.g. since 1000 = 10 x 10 x 10 = 10 ....

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### Natural logarithm - Wikipedia.

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 2.718 281 828 459.The natural logarithm of x is generally written as ln x, log e x, or sometimes, if the base e is implicit, simply log x. Parentheses are sometimes added for clarity, giving ln(x), log e (x), or log(x)..

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### Exponentiation - Wikipedia.

Exponentiation is a mathematical operation, written as b n, involving two numbers, the base b and the exponent or power n, and pronounced as "b raised to the power of n ". When n is a positive integer, exponentiation corresponds to repeated multiplication of the base: that is, b n is the product of multiplying n bases:.

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### Binary logarithm - Wikipedia.

In mathematics, the binary logarithm (log 2 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 ....

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### Isomorphism - Wikipedia.

Examples Logarithm and exponential. Let + be the multiplicative group of positive real numbers, and let be the additive group of real numbers.. The logarithm function: + satisfies = + for all , +, so it is a group homomorphism.The exponential function: + satisfies (+) = () () for all ,, so it too is a homomorphism.. The identities = and = show that and are ....

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### Natural logarithm of 2 - Wikipedia.

The decimal value of the natural logarithm of 2 (sequence A002162 in the OEIS) is approximately The logarithm of 2 in other bases is obtained with the formula = . The common logarithm in particular is (OEIS: A007524) The inverse of this number is the binary logarithm of 10: = (OEIS: A020862). By the Lindemann-Weierstrass theorem, the natural logarithm of ....

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### List of logarithmic identities - Wikipedia.

Explanations. By definition, we know that: = =, where . Setting =, we can see that: = = = =.So, substituting these values into the formula, we see that: = =, which gets us the first property. Setting =, we can see that: = = = =.So, substituting these values into the formula, we see that: = =, which gets us the second property. Many mathematical identities are called trivial , only ....

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### List of Wikipedias - Wikipedia.

Wikipedia is a free multilingual open-source wiki-based online encyclopedia edited and maintained by a community of volunteer editors, started on 15 January 2001 (21 years ago) () as an English-language encyclopedia.Other editions were soon created: the German and Catalan editions were created around 16 March, the French edition was created on 23 March, and the ....

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### Logarithmic scale - Wikipedia.

A logarithmic scale (or log scale) is a way of displaying numerical data over a very wide range of values in a compact way--typically the largest numbers in the data are hundreds or even thousands of times larger than the smallest numbers.Such a scale is nonlinear: the numbers 10 and 20, and 60 and 70, are not the same distance apart on a log scale..

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### Kip Thorne - Wikipedia.

Kip Stephen Thorne (born June 1, 1940) is an American theoretical physicist known for his contributions in gravitational physics and astrophysics.A longtime friend and colleague of Stephen Hawking and Carl Sagan, he was the Richard P. Feynman Professor of Theoretical Physics at the California Institute of Technology (Caltech) until 2009 and is one of the world's leading experts ....

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### Third law of thermodynamics - Wikipedia.

The third law provides an absolute reference point for the determination of entropy at any other temperature. The entropy of a closed system, determined relative to this zero point, is then the absolute entropy of that system. Mathematically, the absolute entropy of any system at zero temperature is the natural log of the number of ground states times Boltzmann's constant k B = ....

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### Discrete logarithm calculator.

In this version of the discrete logarithm calculator only the Pohlig-Hellman algorithm is implemented, so the execution time is proportional to the square root of the largest prime factor of the modulus minus 1. The applet works in a reasonable amount of time if this factor is less than 10 17. I will add the index-calculus algorithm soon..

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### Subtraction - Wikipedia.

Subtraction is an arithmetic operation that represents the operation of removing objects from a collection. Subtraction is signified by the minus sign, -.For example, in the adjacent picture, there are 5 - 2 peaches--meaning 5 peaches with 2 taken away, resulting in a total of 3 peaches. Therefore, the difference of 5 and 2 is 3; that is, 5 - 2 = 3..

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### Hyperbolic functions - Wikipedia.

Hyperbolic tangent. The hyperbolic tangent is the (unique) solution to the differential equation f ? = 1 - f 2, with f (0) = 0.. Useful relations. The hyperbolic functions satisfy many identities, all of them similar in form to the trigonometric identities.In fact, Osborn's rule states that one can convert any trigonometric identity for , , or and into a hyperbolic identity, by expanding ....

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### Lambert W function - Wikipedia.

In mathematics, the Lambert W function, also called the omega function or product logarithm, is a multivalued function, namely the branches of the converse relation of the function f(w) = we w, where w is any complex number and e w is the exponential function.. For each integer k there is one branch, denoted by W k (z), which is a complex-valued function of one complex argument..

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### Complex logarithm - Wikipedia.

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 of a nonzero complex number z, defined to be any complex number w for which e w = z. Such a number w is denoted by log z. If z is given in polar form as z = re i?, where r and ? ....

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### Linear discriminant analysis - Wikipedia.

Linear discriminant analysis (LDA), normal discriminant analysis (NDA), or discriminant function analysis is a generalization of Fisher's linear discriminant, a method used in statistics and other fields, to find a linear combination of features that characterizes or separates two or more classes of objects or events. The resulting combination may be used as a linear classifier, or, more ....

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### Continuous uniform distribution - Wikipedia.

Definitions Probability density function. The probability density function of the continuous uniform distribution is: = { , < >The values of f(x) at the two boundaries a and b are usually unimportant because they do not alter the values of the integrals of f(x) dx over any interval, nor of x f(x) dx or any higher moment. Sometimes they are chosen to be zero, and sometimes chosen ....

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### Logarithmische Normalverteilung – Wikipedia.

Die logarithmische Normalverteilung (kurz Log-Normalverteilung) ist eine kontinuierliche Wahrscheinlichkeitsverteilung fur eine Variable, die nur positive Werte annehmen kann. Sie beschreibt die Verteilung einer Zufallsvariablen, wenn die mit dem Logarithmus transformierte Zufallsvariable = normalverteilt ist. Sie bewahrt sich als Modell fur viele Messgrossen in ....

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### Logarithme naturel — Wikipédia.

Le logarithme naturel ou logarithme neperien, ou encore logarithme hyperbolique jusqu'au XX e siecle, transforme, comme les autres fonctions logarithmes, les produits en sommes.L'utilisation de telles fonctions permet de faciliter les calculs comprenant de nombreuses multiplications, divisions et elevations a des puissances rationnelles..

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