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Most (all?) logs I encountered (in mathematics) were base e, simply due to the fact that base 10 isn't special in mathematics, but for base e, you have log' x =

Most (all?) logs I encountered (in mathematics) were base e, simply due to the fact that base 10 isn't special in mathematics, but for base e, you have log' x = 1/x. Also, it seems very common to denote the inverse of a function (even sine or cosine) with f^-1. See also Wikipedia on that subject (https://en.wikipedia.org/wiki/Logarithm https://en.wikipedia.org/wiki/Logarithm): >The logarithm to base 10 (that is b = 10) is called the common logarithm and has many applications in science and engineering. The natural logarithm has the number e (≈ 2.718) as its base; its use is widespread in mathematics and physics, because of its simpler derivative. The binary logarithm uses base 2 (that is b = 2) and is commonly used in computer science.

iheartmemcache 11y ago
At least in the northeast US, ln(x) was the preferred nomenclature as to eliminate ambiguity. Again, it depends on what course you were taking. Lg and Ln. Log was explicitly avoided. In higher mathematics, f^-1 does not mean the inverse of a function, unless that function is injective. Most people are aware of that at that point, but it's still a mental hurdle you have to unlearn and can lead to dangerous composition errors. (Edit: since I can't respond to you, poster below me, I mean the latter of course) Historically, in yore days of sextants, slide rules and log tables, engineers could "lift" multiplication into addition with said log tables which were of convention base 10. For anyone who wasn't a peer in the Royal Society or a professor, that's how complicated math calculations were performed. Banks balanced books and calculated interest payments via tables like this, and the precision of your log tables had a mantissa (the original floating point error, heh).
- schoen 11y ago
  > f^-1 does not mean the inverse of a function, unless that function is injective Do you mean that it has a different meaning for a non-injective function, or that it's undefined for a non-injective function because the non-injective function does not have an inverse?

iheartmemcache 11y ago

At least in the northeast US, ln(x) was the preferred nomenclature as to eliminate ambiguity. Again, it depends on what course you were taking. Lg and Ln. Log was explicitly avoided. In higher mathematics, f^-1 does not mean the inverse of a function, unless that function is injective. Most people are aware of that at that point, but it's still a mental hurdle you have to unlearn and can lead to dangerous composition errors. (Edit: since I can't respond to you, poster below me, I mean the latter of course) Historically, in yore days of sextants, slide rules and log tables, engineers could "lift" multiplication into addition with said log tables which were of convention base 10. For anyone who wasn't a peer in the Royal Society or a professor, that's how complicated math calculations were performed. Banks balanced books and calculated interest payments via tables like this, and the precision of your log tables had a mantissa (the original floating point error, heh).

schoen 11y ago
> f^-1 does not mean the inverse of a function, unless that function is injective Do you mean that it has a different meaning for a non-injective function, or that it's undefined for a non-injective function because the non-injective function does not have an inverse?