Common logarithm

In mathematics, the common logarithm (aka "standard logarithm") is the logarithm with base 10.[1] 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[2] or logarithmus decadis.[3]

The mathematical notation for using the common logarithm is log(x),[4] log10(x),[5] or sometimes Log(x) with a capital L;[a] on calculators, it is printed as "log",[6] 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.[7]

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.[1] 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.[8] For the history of such tables, see log table.

Numbers are placed on slide rule scales at distances proportional to the differences between their logarithms. By mechanically adding the distance from 1 to 2 on the lower scale to the distance from 1 to 3 on the upper scale, one can quickly determine that 2  ×  3 = 6.
  1. ^ a b Cite error: The named reference Hall_1909 was invoked but never defined (see the help page).
  2. ^ Cite error: The named reference Euler_1748 was invoked but never defined (see the help page).
  3. ^ Cite error: The named reference Scherffer_1772 was invoked but never defined (see the help page).
  4. ^ "Introduction to Logarithms". www.mathsisfun.com. Retrieved 2020-08-29.
  5. ^ Weisstein, Eric W. "Common Logarithm". mathworld.wolfram.com. Retrieved 2020-08-29.
  6. ^ "Using a calculator - Laws of logarithms and exponents - Higher Maths Revision". BBC Bitesize. BBC. Retrieved 2025-07-08.
  7. ^ "Introduction to Logarithms". www.mathsisfun.com. Retrieved 2025-07-08.
  8. ^ Cite error: The named reference Hedrick_1913 was invoked but never defined (see the help page).


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