Common logarithm
the logarithm with base 10, formerly widely used for calculations
In mathematics, the common logarithm (aka "standard logarithm") is the logarithm with base 10. It is also known as the decadic logarithm, the decimal logarithm and the Briggsian logarithm. The name "Briggsian logarithm" is in honor of the British mathematician Henry Briggs who conceived of and developed the values for the "common logarithm". Historically, the "common logarithm" was known by its Latin name logarithmus decimalis or logarithmus decadis.
The mathematical notation for using the common logarithm is log(x), log10(x), or sometimes Log(x) with a capital L; on calculators, it is printed as "log", but mathematicians usually mean natural logarithm (logarithm with base e ≈ 2.71828) rather than common logarithm when writing "log", since the natural logarithm is – contrary to what the name of the common logarithm implies – the most commonly used logarithm in pure math.
Before the early 1970s, handheld electronic calculators were not available, and mechanical calculators capable of multiplication were bulky, expensive, and not widely available. Instead, tables of base-10 logarithms were used in science, engineering and navigation—when calculations required greater accuracy than could be achieved with a slide rule. By turning multiplication and division to addition and subtraction, use of logarithms avoided laborious and error-prone paper-and-pencil multiplications and divisions. Because logarithms were so useful, tables of base-10 logarithms were given in appendices of many textbooks. Mathematical and navigation handbooks included tables of the logarithms of trigonometric functions as well.
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