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?