Wikipedia sez:
The natural logarithm of $x$ is often written "$\ln(x)$", instead of $\log_e(x)$ especially in disciplines where it isn't written "$\log(x)$". However, some mathematicians disapprove of this notation. In his 1985 autobiography, Paul Halmos criticized what he considered the "childish $\ln$ notation," which he said no mathematician had ever used. In fact, the notation was invented by a mathematician, Irving Stringham, professor of mathematics at University of California, Berkeley, in 1893.
Apparently the notation "$\ln$" first appears in Stringham's book Uniplanar algebra: being part I of a propædeutic to the higher mathematical analysis.
But this doesn't explain why "$\ln$" has become so pervasive. I'm pretty sure that most high schools in the US at least still use the notation "$\ln$" today, since all of the calculus students I come into contact with at Berkeley seem to universally use "$\ln$".
How did this happen?
Best Answer
As noted in the original question, 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."