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Mathematical function, inverse of an exponential function
the logarithm of a number is the exponent by which another fixed value, the base, must be raised to produce that number. For example, the logarithm of
Logarithm
Logarithm to the base of the mathematical constant e
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
Natural_logarithm
2.71828...; base of natural logarithms
constant, approximately equal to 2.71828, that is the base of the natural logarithm and exponential function. It is sometimes called Euler's number, after
E_(mathematical_constant)
Mathematical function
the common logarithm (aka "standard logarithm") is the logarithm with base 10. It is also known as the decadic logarithm, the decimal logarithm and the Briggsian
Common_logarithm
Mathematical operation on invertible matrices
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
Logarithm_of_a_matrix
Problem of inverting exponentiation in groups
given real numbers a {\displaystyle a} and b {\displaystyle b} , the logarithm log b ( a ) {\displaystyle \log _{b}(a)} is a number x {\displaystyle
Discrete_logarithm
Exponent of a power of two
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
Binary_logarithm
Development of the mathematical function
The history of logarithms is the story of a correspondence (in modern terms, a group isomorphism) between multiplication on the positive real numbers and
History_of_logarithms
Logarithm of a complex number
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
Complex_logarithm
Topics referred to by the same term
The term integral logarithm may stand for: Discrete logarithm in algebra, Logarithmic integral function in calculus. This disambiguation page lists articles
Integral_logarithm
Mathematical theorem
iterated logarithm describes the magnitude of the fluctuations of a random walk. The original statement of the law of the iterated logarithm is due to
Law_of_the_iterated_logarithm
Tool for a fast finite-field arithmetic
Zech logarithms are used to implement addition in finite fields when elements are represented as powers of a generator α {\displaystyle \alpha } . Zech
Zech's_logarithm
Arithmetic operation
exponents, below), or in terms of the logarithm of the base and the exponential function (§ Powers via logarithms, below). The result is always a positive
Exponentiation
Mathematical function, denoted exp(x) or e^x
{\displaystyle \exp(x+y)=\exp x\cdot \exp y} . Its inverse function, the natural logarithm, ln {\displaystyle \ln } or log {\displaystyle \log } , converts
Exponential_function
Method of multiplying small numbers using lookup tables
The Irish logarithm was a system of number manipulation invented by Percy Ludgate for machine multiplication. The system used a combination of mechanical
Irish_logarithm
Inverse function to a tower of powers
iterated logarithm of n {\displaystyle n} , written log* n {\displaystyle n} (usually read "log star"), is the number of times the logarithm function
Iterated_logarithm
Approach to public-key cryptography
protocols, a central hardness assumption is the elliptic curve discrete logarithm problem (ECDLP): given a public base point P {\displaystyle P} and another
Elliptic-curve_cryptography
Multivalued function in mathematics
mathematics, the Lambert W function, also called the omega function or product logarithm, is a multivalued function, namely the branches of the converse relation
Lambert_W_function
Term in stochastic calculus
In stochastic calculus, stochastic logarithm of a semimartingale Y {\displaystyle Y} such that Y ≠ 0 {\displaystyle Y\neq 0} and Y − ≠ 0 {\displaystyle
Stochastic_logarithm
Mathematical function
The term Napierian logarithm or Naperian logarithm, named after John Napier, is often used to mean the natural logarithm. Napier did not introduce this
Napierian_logarithm
Mathematical operation in calculus
values in the positive reals. For example, since the logarithm of a product is the sum of the logarithms of the factors, we have ( log u v ) ′ = ( log
Logarithmic_derivative
Complex exponential in terms of sine and cosine
{\displaystyle e^{ix}=\cos x+i\sin x,} where e is the base of the natural logarithm, i is the imaginary unit, and cos and sin are the trigonometric functions
Euler's_formula
One of the four basic arithmetic operations
{\text{root}}} Logarithm (log) log base ( anti-logarithm ) = {\displaystyle \scriptstyle \log _{\text{base}}({\text{anti-logarithm}})\,=\,} logarithm {\displaystyle
Subtraction
Mathematical function
As in the complex case, it has an inverse function, named the p-adic logarithm. The usual exponential function on C is defined by the infinite series
P-adic_exponential_function
gets us the second property. Logarithms and exponentials with the same base cancel each other. This is true because logarithms and exponentials are inverse
List of logarithmic identities
List_of_logarithmic_identities
Binary logarithm Bode plot Henry Briggs Bygrave slide rule Cologarithm Common logarithm Complex logarithm Discrete logarithm Discrete logarithm records
Index_of_logarithm_articles
Best results achieved to date
Discrete logarithm records are the best results achieved to date in solving the discrete logarithm problem, which is the problem of finding solutions
Discrete_logarithm_records
Mathematical constant
In mathematics, the natural logarithm of 2 is the unique real number argument such that the exponential function equals two. It appears frequently in
Natural_logarithm_of_2
Method of exchanging cryptographic keys
increases the difficulty for an adversary attempting to compute the discrete logarithm and compromise the shared secret. These two values are chosen in this
Diffie–Hellman_key_exchange
List of values of a mathematical function
in order to simplify and drastically speed up computation. Tables of logarithms and trigonometric functions were common in math and science textbooks
Mathematical_table
Point of interest for complex multi-valued functions
the complex logarithm at the origin. Going once counterclockwise around a simple closed curve encircling the origin, the complex logarithm is incremented
Branch_point
Arithmetic operation
calculated with an abacus. Logarithm tables can be used to divide two numbers, by subtracting the two numbers' logarithms, then looking up the antilogarithm
Division_(mathematics)
Arithmetic operation
called super-root and super-logarithm. They are respectively analogous to the operations of taking nth roots and taking logarithms. None of the three functions
Tetration
Collection of mathematical functions originated by Constantino Tsallis
functions were first introduced in Tsallis statistics in 1994. However, the q-logarithm is the Box–Cox transformation for q = 1 − λ {\displaystyle q=1-\lambda
Tsallis_statistics
Key agreement protocol
selected it), unless that party can solve the elliptic curve discrete logarithm problem. Bob's private key is similarly secure. No party other than Alice
Elliptic-curve_Diffie–Hellman
Arithmetical operation
is tedious and error-prone. Common logarithms were invented to simplify such calculations, since adding logarithms is equivalent to multiplying. The slide
Multiplication
Transforming data by taking the logarithm
unit, it would be common to transform each person's income value by the logarithm function. Guidance for how data should be transformed, or whether a transformation
Log transformation (statistics)
Log_transformation_(statistics)
Deliberate process that transforms inputs to outputs with variable change
{\text{root}}} Logarithm (log) log base ( anti-logarithm ) = {\displaystyle \scriptstyle \log _{\text{base}}({\text{anti-logarithm}})\,=\,} logarithm {\displaystyle
Calculation
Probabilistic algorithm for computing discrete logarithms
is a probabilistic algorithm for computing discrete logarithms. Dedicated to the discrete logarithm in ( Z / q Z ) ∗ {\displaystyle (\mathbb {Z} /q\mathbb
Index_calculus_algorithm
Method of mathematical differentiation
In calculus, logarithmic differentiation or differentiation by taking logarithms is a method used to differentiate functions by employing the logarithmic
Logarithmic_differentiation
Measurement scale based on orders of magnitude
helpful when the data: covers a large range of values, since the use of the logarithms of the values rather than the actual values reduces a wide range to a
Logarithmic_scale
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
Gaussian_logarithm
British mathematician (1561–1630)
changing the original logarithms invented by John Napier into common (base 10) logarithms, which are sometimes known as Briggsian logarithms in his honor. The
Henry_Briggs_(mathematician)
Probability distribution
distribution is a continuous probability distribution of a random variable whose logarithm is normally distributed. Thus, if the random variable X is log-normally
Log-normal_distribution
Scottish mathematician (1550–1617)
the 8th Laird of Merchiston. Napier is best known as the discoverer of logarithms. He also invented the Napier's bones calculating device and popularised
John_Napier
Mathematical result of division
{\text{root}}} Logarithm (log) log base ( anti-logarithm ) = {\displaystyle \scriptstyle \log _{\text{base}}({\text{anti-logarithm}})\,=\,} logarithm {\displaystyle
Quotient
Time for exponential decay to remove half of a quantity
t_{1/2}={\frac {\ln(2)}{\lambda }}=\tau \ln(2)} where ln(2) is the natural logarithm of 2 (approximately 0.693). In chemical kinetics, the value of the half-life
Half-life
Mathematical equation linking e, i and π
}+1=0} where e {\displaystyle e} is Euler's number, the base of natural logarithms, i {\displaystyle i} is the imaginary unit, which by definition satisfies
Euler's_identity
Branch of elementary mathematics
sense, it also includes exponentiation, extraction of roots, and taking logarithms. Arithmetic systems can be distinguished based on the type of numbers
Arithmetic
First publication of complete tables of logarithms, 1614
Wonderful Canon of Logarithms, 1614) and Mirifici Logarithmorum Canonis Constructio (Construction of the Wonderful Canon of Logarithms, 1619) are two books
Mirifici Logarithmorum Canonis Descriptio
Mirifici_Logarithmorum_Canonis_Descriptio
Mathematical form
{\text{root}}} Logarithm (log) log base ( anti-logarithm ) = {\displaystyle \scriptstyle \log _{\text{base}}({\text{anti-logarithm}})\,=\,} logarithm {\displaystyle
Product_(mathematics)
Musical interval unit
by Alexander John Ellis, follow a tradition of measuring intervals by logarithms that began with Juan Caramuel y Lobkowitz in the 17th century. Ellis chose
Cent_(music)
Theorem in complex analysis
{\displaystyle (a,0)} with a > 0 {\displaystyle a>0} and the complex logarithm defined in a neighborhood of this point, and one lets γ {\displaystyle
Monodromy_theorem
Eye chart
estimate visual acuity. The name of the chart is an abbreviation for "logarithm of the Minimum Angle of Resolution". The chart was developed at the National
LogMAR_chart
Logarithmic unit expressing the ratio of physical quantities
ratio, the corresponding change in decibels is defined as ten times the logarithm with base 10 of that ratio. That is, a change in power by a factor of
Decibel
Public-key cryptosystem
"A Public-Key Cryptosystem and a Signature Scheme Based on Discrete Logarithms" (PDF). IEEE Transactions on Information Theory. 31 (4): 469–472. CiteSeerX 10
ElGamal_encryption
Region of the Cartesian plane bounded by a hyperbola and two radii
by a hyperbola. His findings led to the natural logarithm function, once called the hyperbolic logarithm since it is obtained by integrating, or finding
Hyperbolic_sector
Capital city of Scotland
produced figures in science and engineering. John Napier, inventor of logarithms, was born in Merchiston Tower and lived and died in the city. His house
Edinburgh
Generalization of addition, multiplication, exponentiation, tetration, etc.
F_{2}(a,b)=a\cdot b=e^{\ln(a)+\ln(b)}} This is due to the properties of the logarithm. 3 F 3 ( a , b ) = a ln ( b ) = e ln ( a ) ln ( b ) {\displaystyle
Hyperoperation
Measure of the strength of earthquakes
earthquakes, it is essential to understand the Richter scale uses common logarithms simply to make the measurements manageable (i.e., a magnitude 3 quake
Richter_scale
Mathematical algorithm
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
Pollard's rho algorithm for logarithms
Pollard's_rho_algorithm_for_logarithms
Mechanism for authenticating cryptographic keys
Naccache–Stern Paillier Rabin RSA Okamoto–Uchiyama Schmidt–Samoa Discrete logarithm BLS Cramer–Shoup DH DSA ECDH X25519 X448 ECDSA EdDSA Ed25519 Ed448 ECMQV
Web_of_trust
Mathematical functions
using the quadratic formula and then written in terms of the natural logarithm. arsinh x = ln ( x + x 2 + 1 ) − ∞ < x < ∞ , arcosh x = ln ( x
Inverse_hyperbolic_functions
Function in statistics
this, the logit is also called the log-odds since it is equal to the logarithm of the odds p 1 − p {\textstyle {\frac {p}{1-p}}} where p is a probability
Logit
Generalization of the standard Boltzmann–Gibbs entropy
Boltzmann–Gibbs entropy. It is proportional to the expectation of the q-logarithm of a distribution. The concept was introduced in 1988 by Constantino Tsallis
Tsallis_entropy
Topics referred to by the same term
Firewood, logs used for fuel Lumber or timber, converted from wood logs Logarithm, in mathematics Log, LOG or LoG may also refer to: Log (magazine), an
Log
Digital verification standard
on the mathematical concept of modular exponentiation and the discrete logarithm problem. In a digital signature system, there is a keypair involved, consisting
Digital_Signature_Algorithm
Algorithm in computational number theory
algorithm, see Naming below) is an algorithm for solving the discrete logarithm problem. The algorithm was introduced in 1978 by the number theorist John
Pollard's_kangaroo_algorithm
Topics referred to by the same term
Mantissa ( /mænˈtɪsə/) may refer to: Mantissa (logarithm), the fractional part of the common (base-10) logarithm Significand (also commonly called mantissa)
Mantissa
Scale of numbers with a fixed ratio
the common logarithm, usually as the integer part of the logarithm, obtained by truncation. For example, the number 4000000 has a logarithm (in base 10)
Order_of_magnitude
Equation that is satisfied for all values of the variables
the logarithms. The logarithm of the pth power of a number is p times the logarithm of the number itself; the logarithm of a pth root is the logarithm of
Identity_(mathematics)
Difference between logarithm and harmonic series
notation for logarithms. All instances of log ( x ) {\displaystyle \log(x)} without a subscript base should be interpreted as a natural logarithm, also commonly
Euler's_constant
Physics concept
In physics, optical depth or optical thickness is the natural logarithm of the ratio of incident to transmitted radiant power through a material. Thus
Optical_depth
Application of a function to each point in a data set
unit, it would be common to transform each person's income value by the logarithm function. Guidance for how data should be transformed, or whether a transformation
Data transformation (statistics)
Data_transformation_(statistics)
Fifth letter of the Latin alphabet
symbol for set membership in set theory. 𝑒: the base of the natural logarithm. In British Sign Language (BSL), the letter 'e' is signed by extending
E
Arithmetic operation, inverse of nth power
therefore its principal root r also positive, one takes logarithms of both sides (any base of the logarithm will do) to obtain n log b r = log b x hence
Nth_root
Course designed to prepare students for calculus
The general logarithm, to an arbitrary positive base, Euler presents as the inverse of an exponential function. Then the natural logarithm is obtained
Precalculus
Digital signature scheme
first whose security is based on the intractability of certain discrete logarithm problems. It is efficient and generates short signatures. It was covered
Schnorr_signature
Average uncertainty in variable's states
possible values. The choice of base for log {\displaystyle \log } , the logarithm, varies for different applications. Base 2 gives the unit of bits (or
Entropy_(information_theory)
Scientific calculator by Texas Instruments
the original 8). Switching to a new circuit board design introduced a logarithm bug. TI-30Xa (1994): added the constant key to the TI-30X (26 EUUUBAH)
TI-30
Equation in statistical mechanics
equal to 1.380649 × 10−23 J/K, and ln {\displaystyle \ln } is the natural logarithm function (or log base e, as in the image above). In short, the Boltzmann
Boltzmann's_entropy_formula
System that can issue, distribute and verify digital certificates
Naccache–Stern Paillier Rabin RSA Okamoto–Uchiyama Schmidt–Samoa Discrete logarithm BLS Cramer–Shoup DH DSA ECDH X25519 X448 ECDSA EdDSA Ed25519 Ed448 ECMQV
Public_key_infrastructure
Cryptography secured against quantum computers
integer factorization problem, the discrete logarithm problem, or the elliptic-curve discrete logarithm problem. All of these problems could be easily
Post-quantum_cryptography
Bet sizing formula for long-term growth
a sequence of bets by maximizing the long-term expected value of the logarithm of wealth, which is equivalent to maximizing the long-term expected geometric
Kelly_criterion
Computer representation of real numbers
X {\displaystyle X} , is represented in an LNS by two components: the logarithm ( x {\displaystyle x} ) of its absolute value (as a binary word usually
Logarithmic_number_system
Function that can be written as a sum over prime factors
multiplicity, sometimes called sopfr(n), the potency of n or the integer logarithm of n (sequence A001414 in the OEIS). For example: a0(4) = 2 + 2 = 4 a0(20)
Additive_function
Binary elastic collision between two charged particles
{\displaystyle 1/b} thus yields the logarithm of the ratio of the upper and lower cut-offs. This number is known as the Coulomb logarithm and is designated by either
Coulomb_collision
Electrical circuit
A log amplifier, which may spell log as logarithmic or logarithm and which may abbreviate amplifier as amp or be termed as a converter, is an electronic
Log_amplifier
Taylor series for the natural logarithm
series or Newton–Mercator series is the Taylor series for the natural logarithm: ln ( 1 + x ) = x − x 2 2 + x 3 3 − x 4 4 + ⋯ {\displaystyle \ln(1+x)=x-{\frac
Mercator_series
Assumption used in cryptographic systems
computational hardness assumption about a certain problem involving discrete logarithms in cyclic groups. It is used as the basis to prove the security of many
Decisional Diffie–Hellman assumption
Decisional_Diffie–Hellman_assumption
Facts provided or learned about something or someone
probability of occurrence. Uncertainty is proportional to the negative logarithm of the probability of occurrence. Information theory takes advantage of
Information
Root-finding algorithm
{\displaystyle x} to an integer as a way to compute an approximation of the binary logarithm log 2 ( x ) {\textstyle \log _{2}(x)} Use this approximation to compute
Fast_inverse_square_root
Approximation for factorials
Abraham de Moivre. One way of stating the approximation involves the logarithm of the factorial: ln n ! = n ln n − n + O ( ln n ) , {\displaystyle
Stirling's_approximation
Extension of the factorial function
notation for logarithms. All instances of log ( x ) {\displaystyle \log(x)} without a subscript base should be interpreted as a natural logarithm, also commonly
Gamma_function
Mathematical formula involving a given set of operations
that are allowed in closed forms are nth root, exponential function, logarithm, and trigonometric functions. However, the set of basic functions depends
Closed-form_expression
Concept in Fourier analysis
is the result of computing the inverse Fourier transform (IFT) of the logarithm of the estimated signal spectrum. The method is a tool for investigating
Cepstrum
Algorithm for computing logarithms
Silver–Pohlig–Hellman algorithm, is a special-purpose algorithm for computing discrete logarithms in a finite abelian group whose order is a smooth integer. The algorithm
Pohlig–Hellman_algorithm
Continuous stochastic process
Brownian motion, is a continuous-time stochastic process in which the logarithm of the randomly varying quantity follows a Brownian motion with drift
Geometric_Brownian_motion
Set of rules defining correctly structured programs
7183 e: Natural logarithm base Math.LN2 0.69315 Natural logarithm of 2 Math.LN10 2.3026 Natural logarithm of 10 Math.LOG2E 1.4427 Logarithm to the base 2
JavaScript_syntax
Measure of the level of acidity or basicity of an aqueous solution
negative decimal logarithm of", and is used in the term pKa for acid dissociation constants, so pH is "the negative decimal logarithm of H+ ion concentration"
PH
LOGARITHM
LOGARITHM
LOGARITHM
LOGARITHM
Girl/Female
American, British, English, Swedish
Follower of Christ; Christian
Male
Polish
Polish form of Latin Victor, WIKTOR means "conqueror."
Surname or Lastname
English (Staffordshire)
English (Staffordshire) : variant of Leath.
Boy/Male
American, Australian, Chinese, French, Jamaican, Latin, Spanish, Swedish
Enduring; Lasting
Girl/Female
Indian, Sanskrit
Place
Boy/Male
Hindu
God gift, Inherent, Inscribed into something, Within something
Female
Hawaiian
Hawaiian form of Hebrew Rachel, LAHELA means "ewe."Â
Boy/Male
Muslim
Charm
Boy/Male
Indian, Punjabi, Sikh
King's Love
Boy/Male
Hindu, Indian, Latin, Sanskrit
Renowned; Cane
LOGARITHM
LOGARITHM
LOGARITHM
LOGARITHM
LOGARITHM
a.
Alt. of Logarithmetical
n.
The number corresponding to a logarithm. The word has been sometimes, though rarely, used to denote the complement of a given logarithm; also the logarithmic cosine corresponding to a given logarithmic sine.
n.
An expression of the condition of equality between two algebraic quantities or sets of quantities, the sign = being placed between them; as, a binomial equation; a quadratic equation; an algebraic equation; a transcendental equation; an exponential equation; a logarithmic equation; a differential equation, etc.
n.
A logarithm of the cosine or cotangent.
adv.
Logarithmically.
n.
The act of finding out or inventing; contrivance or construction of that which has not before existed; as, the invention of logarithms; the invention of the art of printing.
a.
See Logarithmic.
adv.
By the use of logarithms.
n.
The number from which a mathematical table is constructed; as, the base of a system of logarithms.
a.
Of or pertaining to logarithms; consisting of logarithms.
a.
Alt. of Logarithmical
n.
A number or quantity which is arbitrarily made the fundamental number of any system; a base. Thus, 10 is the radix, or base, of the common system of logarithms, and also of the decimal system of numeration.
n.
Any collection and arrangement in a condensed form of many particulars or values, for ready reference, as of weights, measures, currency, specific gravities, etc.; also, a series of numbers following some law, and expressing particular values corresponding to certain other numbers on which they depend, and by means of which they are taken out for use in computations; as, tables of logarithms, sines, tangents, squares, cubes, etc.; annuity tables; interest tables; astronomical tables, etc.
n.
The integral part (whether positive or negative) of a logarithm.
n.
The decimal part of a logarithm, as distinguished from the integral part, or characteristic.
n.
One of a class of auxiliary numbers, devised by John Napier, of Merchiston, Scotland (1550-1617), to abridge arithmetical calculations, by the use of addition and subtraction in place of multiplication and division.