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> 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. That's not true. The natural logarithm i
by bonzini 6y ago
> 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.
That's not true. The natural logarithm is the only one whose derivative is 1/x but the identity you wrote is true with any base.
People had been using logarithmic tables to do multiplication centuries before Napier came up with "e".
- contravariant 6y agoTrue, although the fact that all of them are pretty much equivalent does mean that there's no real reason to think of it as a logarithm with 'base' anything. Also to the best of my knowledge there's no logarithm tables that predate Napier (1550-1617), and when you try to calculate those tables you naturally stumble upon the natural logarithm (or at least a very close approximation), as the easiest way to create a logarithm table is to start with the powers of something like 1.00000001.
- bonzini 6y agoRight, I am not sure why I thought that the slide rule predated logarithms.