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Topics referred to by the same term
Logarithmic can refer to: Logarithm, a transcendental function in mathematics Logarithmic scale, the use of the logarithmic function to describe measurements
Logarithmic
Measurement scale based on orders of magnitude
A logarithmic scale (or log scale) is a method used to display numerical data that spans a broad range of values, especially when there are significant
Logarithmic_scale
Self-similar growth curve
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
Logarithmic_spiral
Mathematical function, inverse of an exponential function
respectively. Several important formulas, sometimes called logarithmic identities or logarithmic laws, relate logarithms to one another. The logarithm of
Logarithm
Mathematical operation in calculus
In mathematics, specifically in calculus and complex analysis, the logarithmic derivative of a function f is defined by the formula f ′ f {\displaystyle
Logarithmic_derivative
Functions of an angle
functions like the logarithmic sine, logarithmic cosine, logarithmic secant, logarithmic cosecant, logarithmic tangent and logarithmic cotangent. The word
Trigonometric_functions
Measure for the damping of an oscillator
Logarithmic decrement, δ {\displaystyle \delta } , is used to find the damping ratio of an underdamped system in the time domain. The method of logarithmic
Logarithmic_decrement
Type of resistor, usually with three terminals
usually marked with an "A" for logarithmic taper or a "B" for linear taper; "C" for the rarely seen reverse logarithmic taper. Others, particularly those
Potentiometer
Growth at a rate that is a logarithmic function
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)
Logarithmic_growth
Special function defined by an integral
In mathematics, the logarithmic integral function or integral logarithm li(x) is a special function. It is relevant in problems of physics and has number
Logarithmic_integral_function
Meromorphic differential form
In algebraic geometry and the theory of complex manifolds, a logarithmic differential form is a differential form with poles of a certain kind. The concept
Logarithmic_form
Self-similar curve related to golden ratio
In geometry, a golden spiral is a logarithmic spiral whose growth factor is φ, the golden ratio. That is, a golden spiral gets wider (or further from
Golden_spiral
Configurable attenuation circuit
A logarithmic resistor ladder is an electronic circuit, composed of a series of resistors and switches, designed to create an attenuation from an input
Logarithmic_resistor_ladder
{\displaystyle s(t)} and r ( t ) {\displaystyle r(t)} , also known as their logarithmic convolution or log-volution is defined as the function s ∗ l r ( t )
Logarithmic_convolution
Difference of two numbers divided by the logarithm of their quotient
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
Logarithmic_mean
Type of graph
science and engineering, a semi-log plot/graph or semi-logarithmic plot/graph has one axis on a logarithmic scale, the other on a linear scale. It is useful
Semi-log_plot
Search algorithm used in sorted arrays
computer science, binary search, also known as half-interval search, logarithmic search, or binary chop, is a search algorithm that finds the position
Binary_search
Estimate of time taken for running an algorithm
consideration in software engineering. An algorithm is said to take logarithmic time when T ( n ) = O ( log n ) {\displaystyle T(n)=O(\log n)} . Since
Time_complexity
Type of beach with spiral shaped shoreline
A logarithmic spiral beach is a type of beach which develops in the direction under which it is sheltered by a headland, in an area called the shadow
Logarithmic_spiral_beach
algebraic geometry, a logarithmic pair consists of a variety, together with a divisor along which one allows mild logarithmic singularities. They were
Logarithmic_pair
Computer representation of real numbers
A logarithmic number system (LNS) is an arithmetic system used for representing real numbers in computer and digital hardware, especially for digital
Logarithmic_number_system
Mathematical function often applied to matrices
In mathematics, the logarithmic norm is a real-valued functional on operators, constructed from either a vector norm or an inner product, or directly
Logarithmic_norm
Probability distribution
{\displaystyle X} itself. This relationship is true regardless of the base of the logarithmic or exponential function: If log a X {\displaystyle \log _{a}X} is normally
Log-normal_distribution
Gradual change in level of audio signal
A smooth fade is one that changes according to the logarithmic scale, as faders are logarithmic over much of their working range of 30-40 dB. If the
Fade_(audio_engineering)
Method of calculating heat transfer in flow systems
In thermal engineering, the logarithmic mean temperature difference (LMTD) is used to determine the temperature driving force for heat transfer in flow
Logarithmic mean temperature difference
Logarithmic_mean_temperature_difference
The symmetric logarithmic derivative is an important quantity in quantum metrology, and is related to the quantum Fisher information. Let ρ {\displaystyle
Symmetric logarithmic derivative
Symmetric_logarithmic_derivative
Finance term; profit on an investment
to a logarithmic return of 40.55%, while an arithmetic return of −50% is equivalent to a logarithmic return of −69.31%. Advantages of logarithmic return:
Rate_of_return
Measure for evaluating probabilistic forecasts
probability as p, then one can write the logarithmic scoring rule as x ln(p) + (1 − x) ln(1 − p). Note that any logarithmic base may be used, since strictly proper
Scoring_rule
Continuous function whose value increases to infinity
functions are inverse barrier functions and logarithmic barrier functions. Resumption of interest in logarithmic barrier functions was motivated by their
Barrier_function
Function whose composition with the logarithm is convex
In mathematics, a function f {\displaystyle f} is logarithmically convex or superconvex if log ∘ f {\displaystyle {\log }\circ f} , the composition of
Logarithmically convex function
Logarithmically_convex_function
Conformal field theory with logarithmic short distance behavior
a logarithmic conformal field theory (LCFT) is a conformal field theory in which the correlators of the basic fields are allowed to be logarithmic at
Logarithmic conformal field theory
Logarithmic_conformal_field_theory
Step-wise dilution of a substance in solution
constant, this results in a geometric progression of the concentration in a logarithmic fashion. A ten-fold serial dilution could be 1 M, 0.1 M, 0.01 M, 0.001
Serial_dilution
Property of two varying quantities with a constant ratio
In mathematics, two sequences of numbers, often experimental data, are proportional or directly proportional if their corresponding elements have a constant
Proportionality_(mathematics)
Randomized Logarithmic-space (RL), sometimes called RLP (Randomized Logarithmic-space Polynomial-time), is the complexity class of computational complexity
RL_(complexity)
Logarithmic unit expressing the ratio of physical quantities
expresses the ratio of two values of a power or root-power quantity on a logarithmic scale. Two signals whose levels differ by one decibel have a power ratio
Decibel
Measure of quantum entanglement in quantum mechanics
P(\rho )} is an arbitrary LOCC operation over ρ {\displaystyle \rho } The logarithmic negativity is an entanglement measure which is easily computable and
Negativity (quantum mechanics)
Negativity_(quantum_mechanics)
Method of mathematical differentiation
calculus, logarithmic differentiation or differentiation by taking logarithms is a method used to differentiate functions by employing the logarithmic derivative
Logarithmic_differentiation
In mathematics, many logarithmic identities exist. The following is a compilation of the notable of these, many of which are used for computational purposes
List of logarithmic identities
List_of_logarithmic_identities
Semiring arising in tropical analysis
tropical analysis, the log-semiring is the semiring structure on the logarithmic scale, obtained by considering the extended real numbers as logarithms
Log_semiring
In theoretical physics, the logarithmic Schrödinger equation (sometimes abbreviated as LNSE or LogSE) is one of the nonlinear modifications of Schrödinger's
Logarithmic Schrödinger equation
Logarithmic_Schrödinger_equation
Relative deformation of a physical body
other more complex definitions of strain are required, such as stretch, logarithmic strain, Green strain, and Almansi strain. Engineering strain, also known
Strain_(mechanics)
the notion of logarithmic differential form and the related Hodge-theoretic concepts. This idea is one of the foundations of logarithmic geometry and has
Log_structure
Logarithmic unit for ratios of measurements of physical field and power quantities
The neper (symbol: Np) is a logarithmic unit for ratios of measurements of physical field and power quantities, such as gain and loss of electronic signals
Neper
Discrete probability distribution
In probability and statistics, the logarithmic distribution (also known as the logarithmic series distribution or the log-series distribution) is a discrete
Logarithmic_distribution
Property determining comparison and ordering
Richter scale of earthquake intensity. Logarithmic magnitudes can be negative. In the natural sciences, a logarithmic magnitude is typically referred to as
Magnitude_(mathematics)
The following is a list of integrals (antiderivative functions) of logarithmic functions. For a complete list of integral functions, see list of integrals
List of integrals of logarithmic functions
List_of_integrals_of_logarithmic_functions
Algorithm for computing trigonometric, hyperbolic, logarithmic and exponential functions
method in their earlier LOCI-1 (September 1964) and LOCI-2 (January 1965) Logarithmic Computing Instrument desktop calculators, they unsuccessfully accused
CORDIC
Complexity class (logarithmic space)
problems that can be solved by a deterministic Turing machine using a logarithmic amount of writable memory space. Formally, the Turing machine has two
L_(complexity)
Computational complexity
Logarithmic-space) is the complexity class containing decision problems that can be solved by a nondeterministic Turing machine using a logarithmic amount
NL_(complexity)
Subset of real numbers that are greater than zero
measure on the real numbers under the logarithm: it is the length on the logarithmic scale. In fact, it is an invariant measure with respect to multiplication
Positive_real_numbers
Relation of flow speed to wall distance
In fluid dynamics, the law of the wall (also known as the logarithmic law of the wall) states that the average velocity of a turbulent flow at a certain
Law_of_the_wall
differentiation Logarithmic distribution Logarithmic form Logarithmic graph paper Logarithmic growth Logarithmic identities Logarithmic mean Logarithmic number
Index_of_logarithm_articles
Point of interest for complex multi-valued functions
categories: algebraic branch points, transcendental branch points, and logarithmic branch points. Algebraic branch points most commonly arise from functions
Branch_point
level) are logarithmic magnitudes of certain quantities referenced to a standard reference value of the same type. A power level is a logarithmic quantity
Level_(logarithmic_quantity)
1 minus the cosine of an angle
the single angle (θ = 0, 2π, ...) where it is zero—thus, one could use logarithmic tables for multiplications in formulas involving versines. In fact, the
Versine
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
computational complexity, the logarithmic time hierarchy (LH) is the complexity class of all computational problems solvable in a logarithmic amount of computation
LH_(complexity)
Mechanical analog computer
and reading the result. For example, a number to be multiplied on one logarithmic-scale ruler can be aligned with the start of another such ruler to sum
Slide_rule
American stock market index composed of 30 industry leaders
Dow Jones Industrial Average Historical logarithmic graph of the DJIA from 1896 to 2018 Foundation February 16, 1885; 141 years ago (1885-02-16) (as DJA)
Dow_Jones_Industrial_Average
Family of lifetime distributions with decreasing failure rate
In probability theory and statistics, the Exponential-Logarithmic (EL) distribution is a family of lifetime distributions with decreasing failure rate
Exponential-logarithmic distribution
Exponential-logarithmic_distribution
Curve that winds around a central point
^{1/2}} The lituus: r = a φ − 1 / 2 {\displaystyle r=a\varphi ^{-1/2}} The logarithmic spiral: r = a e k φ {\displaystyle r=ae^{k\varphi }} The Cornu spiral
Spiral
Austrian mathematician and theoretical physicist (1844–1906)
the world that the tiny particles really exist. To quote Planck, "The logarithmic connection between entropy and probability was first stated by L. Boltzmann
Ludwig_Boltzmann
German-born theoretical physicist (1879–1955)
second. The physicist Lev Landau ranked physicists from 0 to 5 on a logarithmic scale of productivity and genius, with Newton receiving the highest ranking
Albert_Einstein
System of quantities used in science and their interrelationships
of level is sound pressure level, with the unit of decibel. Units of logarithmic frequency ratio include the octave, corresponding to a factor of 2 in
International System of Quantities
International_System_of_Quantities
Scale of numbers with a fixed ratio
obtained. Differences in order of magnitude can be measured on a base-10 logarithmic scale in "decades" (i.e., factors of ten). For example, there is one
Order_of_magnitude
Natural number
{d+1}{d}}\right)} . The tendency for real-world numbers to grow exponentially or logarithmically biases the distribution towards smaller leading digits, with 1 occurring
1
n-dimensional Euclidean space R n {\displaystyle \mathbb {R} ^{n}} is called logarithmically concave (or log-concave for short) if, for any compact subsets A and
Logarithmically concave measure
Logarithmically_concave_measure
Property of spirals
} denotes the golden ratio; logarithmic spirals with other angles are not golden spirals. Spirals that are not logarithmic have pitch angles that vary
Pitch_angle_of_a_spiral
Measurement of radiant electromagnetic power emitted by an object
magnitude (Mbol) of an object is a logarithmic measure of its total energy emission rate, while absolute magnitude is a logarithmic measure of the luminosity within
Luminosity
Psychophysics of varying the intensity of a stimulus
{S}{S_{0}}}.\,\!} The relationship between stimulus and perception is logarithmic. A logarithmic relationship means that if a stimulus varies as a geometric progression
Weber–Fechner_law
Formula for the derivative of a ratio of functions
x ) | . {\displaystyle \ln |h(x)|=\ln |f(x)|-\ln |g(x)|.} Taking the logarithmic derivative of both sides, h ′ ( x ) h ( x ) = f ′ ( x ) f ( x ) − g ′
Quotient_rule
Measure of the strength of earthquakes
refers to these as "Richter" magnitudes. All magnitude scales retain the logarithmic character of the original and are scaled to have roughly comparable numeric
Richter_scale
Number, approximately 1.618
form of a logarithmic spiral) using quarter-circles with radii from these sequences, differing only slightly from the true golden logarithmic spiral. Fibonacci
Golden_ratio
Type of sequence of numbers
sequence a = (a0, a1, ..., an) of nonnegative real numbers is called a logarithmically concave sequence, or a log-concave sequence for short, if ai2 ≥ ai−1ai+1
Logarithmically concave sequence
Logarithmically_concave_sequence
Plane spiral projected onto the surface of a cone
whose floor projection is a plane spiral. If the floor projection is a logarithmic spiral, it is called conchospiral (from conch). In the x {\displaystyle
Conical_spiral
Class of inequalities
In mathematics, logarithmic Sobolev inequalities are a class of inequalities involving the norm of a function f {\displaystyle f} , its logarithm, and
Logarithmic Sobolev inequalities
Logarithmic_Sobolev_inequalities
Concept in number theory
of the natural numbers may be defined analogously. For example, the logarithmic density of a set A is defined as the limit (if it exists) δ ( A ) = lim
Natural_density
Mathematical constant
is a mathematical constant defined as the unique positive zero of the logarithmic integral function. It is named after Srinivasa Ramanujan and Johann Georg
Ramanujan–Soldner_constant
S-shaped curve
"logistic" (French: logistique), but it is presumably in contrast to the logarithmic curve, and by analogy with arithmetic and geometric. His growth model
Logistic_function
Spanish surrealist artist (1904–1989)
the rhinoceros horn signifies divine geometry because it grows in a logarithmic spiral. Dalí was also fascinated by the Tesseract (a four-dimensional
Salvador_Dalí
Galaxy containing the Solar System
and there is currently no consensus on the nature of its arms. Perfect logarithmic spiral patterns only crudely describe features near the Sun, because
Milky_Way
Mathematical concept
Kawamata and others to families of Calabi–Yau varieties of any dimension. A logarithmic transformation (of order m with center p) of an elliptic surface or fibration
Elliptic_surface
Concept in computer science
In computer science, a doubly logarithmic tree is a tree where each internal node of height 1, the tree layer above the leaves, has two children, and
Doubly_logarithmic_tree
Concept in computational complexity theory
BPL (Bounded-error Probabilistic Logarithmic-space), sometimes called BPLP (Bounded-error Probabilistic Logarithmic-space Polynomial-time), is the complexity
BPL_(complexity)
Formula for the derivative of a product
logarithmic derivative provides a simpler expression of the last form, as well as a direct proof that does not involve any recursion. The logarithmic
Product_rule
Wind model
within the lowest portion of the planetary boundary layer (PBL). The logarithmic profile of wind speeds is generally limited to the lowest 100 m of the
Log_wind_profile
Type of isosceles triangle
and icosahedrons. The golden triangle is used to form some points of a logarithmic spiral. By bisecting one of the base angles, a new point is created that
Golden_triangle_(mathematics)
Logarithmic unit of loudness level
The phon is a logarithmic unit of loudness level for tones and complex sounds. Loudness is measured in sones, a linear unit. Human sensitivity to sound
Phon
Distribution of an uncertain quantity
that all orders of magnitude for the proportion are equally likely, the logarithmic prior, which is the uniform prior on the logarithm of proportion. The
Prior_probability
English polymath (1642–1727)
Cambridge students in 2009. The physicist Lev Landau ranked physicists on a logarithmic scale of productivity and genius ranging from 0 to 5. The highest ranking
Isaac_Newton
List of values of a mathematical function
approximations of logarithmic functions — that is, to compute large logarithmic tables. This was motivated mainly by errors in logarithmic tables made by
Mathematical_table
Study of resources used by an algorithm
regardless of the size of the numbers involved the logarithmic cost model, also called logarithmic-cost measurement (and similar variations), assigns
Analysis_of_algorithms
Online fan theory
A logarithmic graph of user reports to Downdetector over Netflix's mass technical outage on January 7
Conformity_Gate
(1654-1705), a member of the famous Swiss mathematical family. He had studied logarithmic spirals during his life and directed for a spiral and the motto to appear
Eadem_mutata_resurgo
integrals of logarithmic functions List of topics related to π List of trigonometric identities Inverse trigonometric functions Logarithmic identities Summation
List of mathematical identities
List_of_mathematical_identities
Unit for measuring ratios on a logarithmic scale
One decade (symbol dec) is a unit for measuring ratios on a logarithmic scale, with one decade corresponding to a ratio of 10 between two numbers. When
Decade_(log_scale)
Type of computational algorithm
using logarithmic space. Conceptually, this means the Turing machine can keep a constant number of pointers into the input, along with a logarithmic number
Log-space_reduction
Line formed by the real numbers
arithmetic to the geometric composition of angles. Marking the line with logarithmically spaced graduations associates multiplication and division with geometric
Number_line
Study of the relationship of body size to shape, anatomy, physiology, and behavior
remarkable scale symmetry: y = k x a , {\displaystyle y=kx^{a},} or in a logarithmic form, log y = a log x + log k , {\displaystyle \log y=a\log x+\log
Allometry
Comparison of a wide range of brightnesses
As visual perception varies logarithmically, it is helpful to have an appreciation of both illuminance and luminance by orders of magnitude. To help compare
Orders of magnitude (illuminance)
Orders_of_magnitude_(illuminance)
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