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Graph of log 2 x as a function of a positive real number x. In mathematics, the binary logarithm (log 2 n) is the power to which the number 2 must be raised to obtain the value n.
The history of logarithms is the story of a correspondence (in modern terms, a group isomorphism) between multiplication on the positive real numbers and addition on the real number line that was formalized in seventeenth century Europe and was widely used to simplify calculation until the advent of the digital computer.
Binary logarithms are also used in computer science, where the binary system is ubiquitous; in music theory, where a pitch ratio of two (the octave) is ubiquitous and the number of cents between any two pitches is a scaled version of the binary logarithm, or log 2 times 1200, of the pitch ratio (that is, 100 cents per semitone in conventional ...
A similar LNS named "signed logarithmic number system" (SLNS) was described in 1975 by Earl Swartzlander and Aristides Alexopoulos; rather than use two's complement notation for the logarithms, they offset them (scale the numbers being represented) to avoid negative logs. [3]
Visual representation of the Logarithmic timeline in the scale of the universe. This timeline shows the whole history of the universe, the Earth, and mankind in one table. . Each row is defined in years ago, that is, years before the present date, with the earliest times at the top of the ch
A page from Henry Briggs' 1617 Logarithmorum Chilias Prima showing the base-10 (common) logarithm of the integers 0 to 67 to fourteen decimal places. In 1616 Briggs visited Napier at Edinburgh in order to discuss the suggested change to Napier's logarithms. The following year he again visited for a similar purpose.
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Unlike rational number arithmetic, real number arithmetic is closed under exponentiation as long as it uses a positive number as its base. The same is true for the logarithm of positive real numbers as long as the logarithm base is positive and not 1. [105] Irrational numbers involve an infinite non-repeating series of decimal digits.