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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.



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