# Why is natural logarithm abbreviated to ln? [closed]

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?

• – tchrist
Commented Feb 8, 2020 at 15:16
• I'm voting to close this question as off-topic because this isn't about the English language. Besides, it is already answered on HSM. Commented Feb 8, 2020 at 15:48
• The real reason is that engineers and others use log to mean "base-10 logarithm", so that log 2 would be a different number than ln 2 because log and ln are different functions, with different values. Commented Feb 8, 2020 at 17:34

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.

• I'm 50% convinced that this belongs on Maths rather than here. Commented Feb 8, 2020 at 14:34
• 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. Commented Feb 8, 2020 at 15:02
• @EdwinAshworth or HSM for that matter. 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