logarithm
Sign in to saveright|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 .
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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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Article
41 sectionsContents
- 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 .