logarithm

Also known as log, logarithmic function, logarithm function, logarithms

right|thumb|upright=1.35|Plots of logarithm functions, with three commonly used bases. The special points are indicated by dotted lines, and all curves intersect in .

AI overview

A logarithm is a mathematical function that answers the question "what power do I need to raise a base number to in order to get another number?" — for example, the logarithm of 100 to base 10 is 2, because 10 raised to the power of 2 equals 100. Logarithms are useful in science, engineering, and everyday applications because they help simplify calculations involving very large or very small numbers and appear naturally in many real-world phenomena.

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Wikidata facts

Image: Mplwp log2e10.svg

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Commons category: Logarithm
Commons gallery: Logarithm
described at URL: tutorial.math.lamar.edu/classes/calci/explogeqns.aspx
Stack Exchange tag: stackoverflow.com/tags/logarithm

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~52 min read

Article

41 sections

Contents

Motivation
Definition
Examples
Logarithmic identities
Product, quotient, power, and root
Particular bases<span class="anchor" id="log_base_anchor"></span>
History
<span class="anchor" id="Antilogarithm"></span>Logarithm tables, slide rules, and historical applications
Log tables
Computations
Slide rules
Analytic properties
Existence
Characterization by the product formula
Graph of the logarithm function
Derivative and antiderivative
Integral representation of the natural logarithm
Transcendence of the logarithm
Calculation
Power series
Taylor series
Inverse hyperbolic tangent
Arithmetic–geometric mean approximation
Feynman's algorithm
Applications
Logarithmic scale
Psychology
Probability theory and statistics
Computational complexity
Entropy and chaos
Fractals
Music
Number theory
Generalizations
Complex logarithm
Inverses of other exponential functions
Related concepts
See also
Notes
References
External links

right|thumb|upright=1.35|Plots of logarithm functions, with three commonly used bases. The special points are indicated by dotted lines, and all curves intersect in .

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 to base is , because is to the rd power: . More generally, if , then is the logarithm of to base , written , so . As a single-variable function, the logarithm to base is the inverse of exponentiation with base .