Editing Common logarithm (section)

{{Short description|Mathematical function}}
{{More citations needed|date=August 2020}}[[File:Graph of common logarithm.svg|right|thumb|alt=The graph shows that log base ten of x rapidly approaches minus infinity as x approaches zero, but gradually rises to the value two as x approaches one hundred.|A graph of the common logarithm of numbers from 0.1 to 100]]

In [[mathematics]], the '''common logarithm''' (aka "standard logarithm") is the [[logarithm]] with base 10.<ref name="Hall_1909"/> 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 (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''<ref name="Euler_1748"/> or ''logarithmus decadis''.<ref name="Scherffer_1772"/>

The mathematical notation for using the common logarithm is {{math|log(''x'')}},<ref>{{Cite web|title=Introduction to Logarithms|url=https://www.mathsisfun.com/algebra/logarithms.html|access-date=2020-08-29|website=www.mathsisfun.com}}</ref> {{math|log<sub>10</sub>(''x'')}},<ref name=":0">{{Cite web|last=Weisstein|first=Eric W.|title=Common Logarithm|url=https://mathworld.wolfram.com/CommonLogarithm.html|access-date=2020-08-29|website=mathworld.wolfram.com|language=en}}</ref> or sometimes {{math|Log(''x'')}} with a capital {{Math|L}};{{refn|group=lower-alpha|The notation {{math|Log}} is ambiguous, as this can also mean the complex natural logarithmic [[multi-valued function]].}} on [[calculator]]s, it is printed as "log", but mathematicians usually mean [[natural logarithm]] (logarithm with base {{mvar|e}} ≈ 2.71828) rather than common logarithm when writing "log".

[[File:APN2002 Table 1, 1000-1500.agr.tiff|thumb|300px|Page from a table of common logarithms. This page shows the logarithms for numbers from 1000 to 1509 to five decimal places. The complete table covers values up to 9999.]]
Before the early 1970s, handheld electronic calculators were not available, and [[mechanical calculator]]s capable of multiplication were bulky, expensive and not widely available. Instead, [[mathematical table|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.<ref name="Hall_1909"/> Because logarithms were so useful, [[mathematical table|table]]s of base-10 logarithms were given in appendices of many textbooks. Mathematical and navigation handbooks included tables of the logarithms of [[trigonometric function]]s as well.<ref name="Hedrick_1913"/> For the history of such tables, see [[log table]].