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A logarithm is the inverse function of exponentiation, which means that it gives the exponent to which a base must be raised to produce a number. Learn about the history, types, formulas, and uses of logarithms in mathematics, science, and engineering.
Learn about the properties and formulas of logarithms, such as the log laws, the change of base formula, and the trivial identities. See derivations, explanations, and examples of how to use logarithms for computational purposes.
The natural logarithm of a number is its logarithm to the base of the mathematical constant e, which is an irrational and transcendental number. The natural logarithm of x is generally written as ln x, loge x, or simply log x, and has various properties and applications in mathematics.
A common logarithm is the logarithm with base 10, also known as the decadic or decimal logarithm. It is indicated by log (x), log10(x), or lg (x) and has the property that the logarithm of numbers differing by a power of 10 have the same fractional part.
Learn how logarithms were invented by John Napier and Henry Briggs in the 16th and 17th centuries, and how they were used to simplify calculations in trigonometry, astronomy, and navigation. Discover the origins and applications of natural logarithms, common logarithms, and slide rules.
Learn the definition, properties and applications of the logarithmic derivative of a function, which is the infinitesimal relative change in it. Find examples of logarithmic derivatives in calculus, complex analysis, mathematical finance and numerical analysis.
A discrete logarithm is an integer that satisfies a power equation in a group. Learn the definition, examples, properties and algorithms of discrete logarithms, and their applications in cryptography.
In science and engineering, a log–log graph or log–log plot is a two-dimensional graph of numerical data that uses logarithmic scales on both the horizontal and vertical axes. Power functions – relationships of the form y = a x k {\displaystyle y=ax^{k}} – appear as straight lines in a log–log graph, with the exponent corresponding to ...
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