In mathematics, the natural logarithm operator is abbreviated as ln. There is no letter n in the word logarithm, so why do we abbreviate in this way?


1 Answer 1


From BetterExplained.com:

Speaking of fancy, the Latin name is logarithmus naturali[s], giving the abbreviation ln.

MathematicsSE has the question 'How did the notation ln for log base e become so pervasive?'. Dan Velleman posts:

... Wikipedia claims that the ln notation was invented by Stringham in 1893. I have seen this claim in other places as well. However, I recently came across an earlier reference. In 1875, in his book Lehrbuch der Mathematik, Anton Steinhauser suggested denoting the natural logarithm of a number a by "log. nat. a (spoken: logarithmus naturalis a) or ln. a" (p. 277). This lends support to the theory that "ln" stands for "logarithmus naturalis."

There is little there in the way of an answer to why the usage became well established.

  • 1
    I'm 50% convinced that this belongs on Maths rather than here. Commented Feb 8, 2020 at 14:34
  • 1
    Why did the usage become well established? It used to be that in scientific (not necessarily mathematical) literature, log a stood for log base 10. So a different notation for log base e was necessary. See the Math.SE question quoted in the answer above. Why did we chose ln instead of something else? Maybe ln was suggested first. Commented Feb 8, 2020 at 14:57
  • I am only 2.718281828459+ % sure.
    – rajah9
    Commented Feb 8, 2020 at 15:02
  • @EdwinAshworth or HSM for that matter.
    – Spencer
    Commented Feb 8, 2020 at 15:45
  • @Spencer Yes, that seems an even better fit. Though both have a 'terminology' tag. ... They can bunfight over terrirory. Commented Feb 8, 2020 at 15:52

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