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Common logarithm

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 is the logarithm with base 10.[1] It is also known as the decadic logarithm and as the decimal logarithm, named after its base, or Briggsian logarithm, after Henry Briggs, an English mathematician who pioneered its use, as well as standard logarithm. Historically, it was known as logarithmus decimalis[2] or logarithmus decadis.[3] It is indicated by log(x),[4] log10(x),[5] or sometimes Log(x) with a capital L;[note 1] 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". To mitigate this ambiguity, the ISO 80000 specification recommends that log10(x) should be written lg(x), and loge(x) should be ln(x).

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

  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. ^ Cite error: The named reference Hedrick_1913 was invoked but never defined (see the help page).


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