> And there's just 1 logarithm, which has the property log(x^y) = y log(x). You don't need the ones with a different base.
Maybe I misunderstood your comment but it really sounds like you're saying that only the natural logarithm has this property, but in fact it's true with every base:
log(x^y; b) = log(x^y)/log(b) = y log(x) / log(b) = y log(x; b)
Rejigging their text slightly, what they said was "There's only one useful logarithm. It has this property. It's the only useful logarithm."
Yes I noticed their use of a comma (and "which" rather than "that"), in fact that's why I added the disclaimer at the start of my comment about possibly misunderstanding theirs. But sandwiching a mention of that property in the middle of making the same point twice only makes sense if it's a supporting argument.
Maybe I misunderstood your comment but it really sounds like you're saying that only the natural logarithm has this property, but in fact it's true with every base:
log(x^y; b) = log(x^y)/log(b) = y log(x) / log(b) = y log(x; b)