This has been irritating me lately. Here is my conception of the world of logarithms:
In grade school, “log” meant a base-10 logarithm. This teaching is moronic and should be stopped. Assuming the world is base-10 is about as useful as assuming the world is English.
In higher education, “log” is the base-e logarithm or natural logarithm, as it were. This is what everybody should think when they see “log” and it should be what’s used anytime a bare log(x) function occurs in a given mathematical, engineering, or scientific system. Natural logarithms should not be “ln” or “lgn” or “logn” or other bastardizations, and if somebody needs a base-10 logarithm, it should be extracted via dividing by a log of 10, or using a two-parameter log function that accepts a base. Notationally, log x n is then the base-x logarithm, and that’s cool.
“lg” is the little bastard child of computer science. It’s not an abbreviation for “log” it’s a shorthand for a base-2 logarithm. Thus “lg 2 n” is completely redundant (on first glance, far more insidious in truth, more on that shortly) and unnecessary. Worse yet is being ignorant enough to suggest that “lg” means a decimal or natural logarithm.
While at UIUC, these were very clearly the rules of how “log” and “lg” worked, in the schools of mathematics, physics, computer science, and electrical engineering. At least that’s what I remember.
Mathworld would seem to agree with me regarding lg, and in fact points out the terrible danger of notations such as lg 2 n, in that they have cryptic and different meanings in number theory. Mathworld goes on further to note that yeah, you’re completely fucked, because even we use the wrong notation, but if you’re doing serious work, log means natural logarithm.
I don’t get why texts of all kinds persist in even considering log to mean a base-10 logarithm. And please, for god’s sake, unless you’re a number theorist (yes, if you’re wondering, I’m pissing on Stephen Dewhurst, whose so far otherwise good C++ Common Knowledge is ignorantly sprinkled with this), don’t go anywhere near lg 2 n.