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

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

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...

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...

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...

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...

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...

Euler: the binary logarithm of a frequency ratio of two musical tones gives the number of octaves by which the tones differ. Binary logarithms can be used to...

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

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

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

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

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

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

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...

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...

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

more. As of November 2024[update], the fastest supercomputer is El Capitan. Starting with known special cases, the calculation of logarithms and trigonometric...

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

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

}\left(1+{\frac {x}{n}}\right)^{n}.} By continuity of the logarithm, this can be proved by taking logarithms and proving x = lim n → ∞ ln ⁡ ( 1 + x n ) n =...

property characterizes logarithms, and it was mathematical fashion to call such a function A ( x ) {\displaystyle A(x)} a logarithm. In particular when we...

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

changing the original logarithms invented by John Napier into common (base 10) logarithms, which are sometimes known as Briggsian logarithms in his honor. The...

other than James I, that Hume applauds is John Napier of Merchiston, the inventor of logarithms. However Napier, Newton and James I are criticised for...

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

exponentiation, extraction of roots, and taking logarithms. Arithmetic systems can be distinguished based on the type of numbers they operate on. Integer...

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