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Chapter 5 presents four problems in proportionality and their solution using Napier's logarithms. He concludes by asking "how great a benefit is bestowed by these logarithms : since by the addition of these for multiplication, by subtraction for divisional, by division by two for the extraction of square roots, and by three for cube roots ...
Logarithms can be used to make calculations easier. For example, two numbers can be multiplied just by using a logarithm table and adding. These are often known as logarithmic properties, which are documented in the table below. [2] The first three operations below assume that x = b c and/or y = b d, so that log b (x) = c and log b (y) = d.
The discrete logarithm problem is considered to be computationally intractable. That is, no efficient classical algorithm is known for computing discrete logarithms in general. A general algorithm for computing log b a in finite groups G is to raise b to larger and larger powers k until the desired a is found.
The implementation used 2000 CPU cores and took about 6 months to solve the problem. [ 40 ] On 16 June 2020, Aleksander Zieniewicz (zielar) and Jean Luc Pons ( JeanLucPons ) announced the solution of a 114-bit interval elliptic curve discrete logarithm problem on the secp256k1 curve by solving a 114-bit private key in Bitcoin Puzzle ...
Scientific quantities are often expressed as logarithms of other quantities, using a logarithmic scale. For example, the decibel is a unit of measurement associated with logarithmic-scale quantities. It is based on the common logarithm of ratios—10 times the common logarithm of a power ratio or 20 times the common logarithm of a voltage ratio.
Pollard's rho algorithm for logarithms is an algorithm introduced by John Pollard in 1978 to solve the discrete logarithm problem, analogous to Pollard's rho algorithm to solve the integer factorization problem.