Research any topic before you write.

Find related topics. | Discover entities. | See connections. | Build a topical map.

Logarithm

In mathematics, 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 1000 to base 10 is 3, because 1000 is 10 to the 3rd power: 1000 = 103 = 10 × 10 × 10. More generally, if x = by, then y is the logarithm of x to base b, written logb x = y, so log10 1000 =…

Measurement, History, Applications & Products

Use the mouse wheel or two fingers (on touchscreens) to zoom in and out of the map.

Research this topic

Explore the main themes, entities and connections around Logarithm. Start with the topic map, then use the sections below for research and deeper semantic analysis.

Explore this topic

Start with a few of the strongest sections from the source topic. These are research directions, not a list of keywords you must use.

Topics to explore

Browse the full topic structure. Each item opens a new analysis centered on that subject.

Overview

Motivation

Logarithmic identities

Particular bases

History

Logarithm tables, slide rules, and historical applications

Analytic properties

Calculation

Applications

Generalizations

Advanced semantic analysis

Deeper signals for content research, entity SEO and topical coverage. The plain-language headings explain what each technical view is useful for.

Map overview Semantic statistics

Logarithm

Nodes311
Edges310
Triples210
Avg. degree1.99
Density0.006431
Components1

How this topic connects Entity context

See the strongest relationship patterns around the current topic before diving into the raw triples.

Logarithm

Top relations

related to External links · 26
Logarithm → Cambridge University Press, Chisholm, Colin Byfleet, December, Educational, EMS Press, Encyclopedia, Encyclopædia Britannica, Eric, History, Hugh, James Whitbread Lee, Logarithmic, Logarithms, Mathematics, MathWorldKhan Academy, Media, Napier's, October, Translation
related to history · 17
Logarithm → Archimedes, Description, Europe, Greek, John Napier, Jost Bürgi, Logarithms, Middle Latin, Mirifici Logarithmorum Canonis Descriptio, Napier, Napier's, Prior, Some, Speaking, Such, The, Wonderful Canon
has application · 16
Logarithm → As, Benford's, By, Fenske, For, Logarithmic, Logarithms, Moreover, Nernst, Nowadays, Pierre-Simon Laplace, Some, The, They, This, Tsiolkovsky
related to Psychology · 10
Logarithm → Fechner, Fitts's, Hick's, In, Increasing, Logarithms, Psychological, Stevens's, This, Weber
related to Feynman's algorithm · 9
Logarithm → Any, Because, Connection Machine, It, Los Alamos National Laboratory, Manhattan Project, Richard Feynman, The, While
related to Log tables · 9
Logarithm → Base-10, Briggs, Henry Briggs, Napier's, Subsequently, Tables, The, These, Thus
related to Logarithmic scale · 9
Logarithm → Apparent, For, In, It, Richter, Scientific, The, This, Vinegar
is a · 8
Logarithm → example of a transcendental function, increasing function, integer n solving the equation b n, inverse operation of exponentiation, monotonic function, monotonic function.ComputationsThe product and quotient of two positive numbers c and d were routinely calculated as the sum and difference of their logarithms, multi-valued inverse of the complex exponential function, multi-valued inverse of the exponential function in finite groups
related to Inverses of other exponential functions · 8
Logarithm → Another, Both, Exponentiation, For, In, Its, Taylor, The
related to Music · 8
Logarithm → Accordingly, B-flat, For, Hz, In, Logarithms, The, Western

Important terminology Word statistics

Use these terms to understand the vocabulary surrounding the topic, not as a checklist for keyword stuffing.

Important terminology

function logarithms displaystyle log number ln base example used 10 inverse frac logarithmic power natural series real called exponential also

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Logarithmis amulti-valued inverse of the complex exponential function0.90text
Logarithmis amulti-valued inverse of the exponential function in finite groups0.90text
Logarithmis ainverse operation of exponentiation0.90text
Logarithmis amonotonic function.ComputationsThe product and quotient of two positive numbers c and d were routinely calculated as the sum and difference of their logarithms0.90text
Logarithmis amonotonic function0.90text
Logarithmis aexample of a transcendental function0.90text
Logarithmis aincreasing function0.90text
Logarithmis ainteger n solving the equation b n0.90text
prosthaphaeresisinstance ofand looking up the antilogarithm is much faster than performing the multiplication by earlier methods0.80text
which relies on trigonometric identities.Calculations of powersinstance ofand looking up the antilogarithm is much faster than performing the multiplication by earlier methods0.80text
roots are reduced to multiplications or divisionsinstance ofand looking up the antilogarithm is much faster than performing the multiplication by earlier methods0.80text
lookups by c dinstance ofand looking up the antilogarithm is much faster than performing the multiplication by earlier methods0.80text

Related concept clusters Concept neighborhoods

These clusters group vocabulary that occurs around closely connected concepts in the source material.

    Connections between topic areas Semantic bridges

    Bridges can reveal useful research angles that are easy to miss in a flat list of related terms.

    Min side: 3
    For writers, content strategists, SEOs, marketers and creators — from quick topic research to advanced semantic analysis.