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Reference.org
Common logarithm
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<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, the common logarithm (aka "standard logarithm") is the <a href="/facts/Logarithm/QeXaV97q">logarithm</a> 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 <a href="/facts/Henry_Briggs_(mathematician)/ctMJIVNG">Henry Briggs</a> who conceived of and developed the values for the "common logarithm". Historically', the "common logarithm" was known by its Latin name <i>logarithmus decimalis</i> or <i>logarithmus decadis</i>. </p><p>The mathematical notation for using the common logarithm is log(<i>x</i>), log10(<i>x</i>), or sometimes Log(<i>x</i>) with a capital L; on <a href="/facts/Calculator/eeLfRS8L">calculators</a>, it is printed as "log", but mathematicians usually mean <a href="/facts/Natural_logarithm/PnreKEzI">natural logarithm</a> (logarithm with base e ≈ 2.71828) rather than common logarithm when writing "log". To mitigate this ambiguity, the <a href="/facts/ISO_80000-2/k1nrIjMW">ISO 80000 specification</a> recommends that log10(<i>x</i>) should be written lg(<i>x</i>), which unfortunately is used for the <a href="/facts/Base-2_logarithm/Uy7kAtRm">base-2 logarithm</a> by CLRS and Sedgwick and <i><a href="/facts/The_Chicago_Manual_of_Style/7g2EwHGA">The Chicago Manual of Style</a></i>, while log<i>e</i>(<i>x</i>) should be ln(<i>x</i>). </p> <p>Before the early 1970s, handheld electronic calculators were not available, and <a href="/facts/Mechanical_calculator/As7HE5dB">mechanical calculators</a> capable of multiplication were bulky, expensive and not widely available. Instead, <a href="/facts/Mathematical_table/uCAtPzJo">tables</a> of base-10 logarithms were used in science, engineering and navigation—when calculations required greater accuracy than could be achieved with a <a href="/facts/Slide_rule/KzIEdWad">slide rule</a>. 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, <a href="/facts/Mathematical_table/uCAtPzJo">tables</a> of base-10 logarithms were given in appendices of many textbooks. Mathematical and navigation handbooks included tables of the logarithms of <a href="/facts/Trigonometric_function/czej7ur0">trigonometric functions</a> as well. For the history of such tables, see <a href="/facts/Log_table/uCAtPzJo">log table</a>. </p>