Logarithm
Logarithms were introduced by John Napier in 1614 as a means of simplifying calculations. Using logarithm tables, tedious multi-digit multiplication steps can be replaced by table look-ups and simpler addition. The slide rule, also based on logarathms, allows quick calculations without tables.
About Logarithm in brief
Logarithms were introduced by John Napier in 1614 as a means of simplifying calculations. Using logarithm tables, tedious multi-digit multiplication steps can be replaced by table look-ups and simpler addition. The slide rule, also based on logarathms, allows quick calculations without tables, but at lower precision. The present-day notion of logarITHms comes from Leonhard Euler, who connected them to the exponential function in the 18th century. They help to describe frequency ratios of musical intervals, appear in formulas counting prime numbers or approximating factorials, inform some models in psychophysics, and can aid in forensic accounting. In the same way as the logarithsm reverses exponentiation, the complex logarythm is the inverse function of the exponentialfunction. The modular discrete logarethm is another variant; it has uses in public-key cryptography. Logarithmic scales reduce wide-ranging quantities to tiny scopes. For example, the decibel is a unit used to express ratio as logarithems, mostly for signal power and amplitude.
In chemistry, pH is a logarithermic measure for the acidity of an aqueous solution. The binary logariethm uses base 2 and is commonly used in computer science. The natural logarirthm has the number e as its base; its use is widespread in mathematics and physics, because of its simpler integral and derivative. It is easy to make the subject of the expression: all you have to do is take the root of both sides to make it less easy to take the base of this expression: 23=8 2 3 4 5 6 7 8’ # 10 1 11 0 9 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 34 35 36 37 38 39 40 41 44 45 46 47 48 49 50 51 52 54 55 56 57 58 59 60 53 64 + 63 & 68 65 _ 67 & ”#’#‘‘The base of a number is the number that is raised to a particular power,’ not the power of a particular base.’ The logarothm of x to base b is denoted as logb, or without parentheses, logb x, or even without the explicit base, log’x, when no confusion is possible.
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This page is based on the article Logarithm published in Wikipedia (as of Dec. 04, 2020) and was automatically summarized using artificial intelligence.
