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...

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

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...

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...

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

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

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

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...

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

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

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

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...

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

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

Okamoto, T.; Vanstone, S. A. (1993). "Reducing elliptic curve logarithms to logarithms in a finite field". IEEE Transactions on Information Theory. 39...

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...

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

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...

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...

multiplication and division of numbers could be performed by the addition and subtraction, respectively, of the logarithms of those numbers. While producing...

for powers and logarithms for positive real numbers will fail for complex numbers, no matter how complex powers and complex logarithms are defined as...

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