Now the error: In the paragraph beginning "By converting numbers into their logarithm", log(4)=2 should be log2(4)=2 - it's been a while since I was in mathematics academically, but isn't it a necessity to show the base of the log if it's not 10?
Which base gets to be special depends. Log on its own often means base e; sometimes base 10; and sometimes base 2 (and sometimes 'base whatever, it's not important')
This article would be better if showed the base in its notation, but for the most part the bases are determinant in context of each paragraph, and that's roughly par for the slide rule course.
My primary use for logarithms today is verifying how many bits an intermediate calculation is going to need on a calculator without base-2 logs. The base conversion algorithm doesn't care what intermediate base you use as long as they match: bits ~= log2(x) == log10(x) / log10(2) == ln(x) / ln(2).
The article says: "In the world of 2s, log(x) tells you how many times you have to multiply 2 by itself to get x."