The history of logarithms is the story of a correspondence (in modern terms, a group isomorphism) between multiplication on the positive real numbers...

relate logarithms to one another. The logarithm of a product is the sum of the logarithms of the numbers being multiplied; the logarithm of the ratio of two...

taken to mean the "logarithms" as originally produced by Napier, it is a function given by (in terms of the modern natural logarithm): N a p L o g ( x...

use of logarithms avoided laborious and error-prone paper-and-pencil multiplications and divisions. Because logarithms were so useful, tables of base-10...

known as the mantissa. Tables of common logarithms typically included only the mantissas; the integer part of the logarithm, known as the characteristic...

Representations of e El Gamal discrete log cryptosystem Harmonic series History of logarithms Hyperbolic sector Iterated logarithm Otis King Law of the iterated...

algorithms called logarithms that economized arithmetic by rendering multiplications into additions. So F was first known as the hyperbolic logarithm. After Euler...

already compiled a table of what in fact were effectively natural logarithms in 1619. It has been said that Speidell's logarithms were to the base e, but...

application of binary logarithms was in music theory, by Leonhard Euler: the binary logarithm of a frequency ratio of two musical tones gives the number of octaves...

function to the transcendental function ex. To accommodate the case of negative logarithms and the corresponding negative hyperbolic angles, different hyperbolic...

logarithms, which follows these steps: scale down, take logarithms, add, take inverse logarithm, scale up. It is no surprise that the originators of logarithms...

of logarithms, high accuracy numerical calculations involving multiplication, division and root extraction were laborious and error prone. Logarithms...

studied how to compute logarithms by geometrical methods and calculated a quantity that, in retrospect, is the base-10 logarithm of e, but he did not recognize...

Baker's theorem gives a lower bound for the absolute value of linear combinations of logarithms of algebraic numbers. Nearly fifteen years earlier, Alexander...

interacted with the topic of planetary motion. Kepler's calculations were made simpler by the contemporaneous invention of logarithms by John Napier and Jost...

fully understand complex logarithms. Euler also suggested that complex logarithms can have infinitely many values. The view of complex numbers as points...

Hindu mathematical traditions as part of the biographical memoir on John Napier and the history of logarithms. The biography project appears to have...

of Merchiston. John Napier is best known as the discoverer of logarithms. He also invented the so-called "Napier's bones" and made common the use of the...

Bürgi's logarithms in the introduction to his Rudolphine Tables (1627): "... as aids to calculation Justus Byrgius was led to these very logarithms many...

logarithms (also known as Jacobi logarithms), but uses a system of indices original to Ludgate. Ludgate's algorithm compresses the multiplication of two...

is a probabilistic algorithm for computing discrete logarithms. Dedicated to the discrete logarithm in ( Z / q Z ) ∗ {\displaystyle (\mathbb {Z} /q\mathbb...

intervals. The representation of musical intervals by logarithms is almost as old as logarithms themselves. Logarithms had been invented by Lord Napier...

and more. As of April 2023[update], the fastest supercomputer is Frontier. Starting with known special cases, the calculation of logarithms and trigonometric...

The history of logic deals with the study of the development of the science of valid inference (logic). Formal logics developed in ancient times in India...

values in the positive reals. For example, since the logarithm of a product is the sum of the logarithms of the factors, we have ( log ⁡ u v ) ′ = ( log ⁡ u...

gases such as temperature in terms of the random motions of large numbers of particles. The field of the history of probability itself was established...

use the completeness of the real numbers, which is not an algebraic property). This article describes the history of the theory of equations, referred...

"Madhava of Sangamagramma". MacTutor History of Mathematics Archive. Pearce, Ian G. (2002). "Madhava of Sangamagramma". MacTutor History of Mathematics...

baseline using wooden rods, a telescope (for his angular measurements), and logarithms (for computation). Gian Domenico Cassini then his son Jacques Cassini...

differentiation by taking logarithms is a method used to differentiate functions by employing the logarithmic derivative of a function f, ( ln ⁡ f ) ′...