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Your thoughts?

- Thread starter Mike_Bson
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Your thoughts?

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(Sorry, I couldn't resist!)

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1. Calculus courses do still teach the derivative of say the base 10 log, but unsurprisingly it's obtained by first converting to the natural log.

2. In complex analysis, it's important to distinguish log as a potentially multi-valued complex function (i.e. when we don't define the principal branch) versus taking the real-valued natural logarithm. Here, I always write [itex]\log (re^{i\theta}) = \ln r + i\theta + 2\pi i k,[/itex] because it is actually quite easy to screw this up.

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nicksauce

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arildno

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I do see, however, that the most natural logarithm may have an even stronger claim on the notation log(x), or lg(x) than the logarithm that was first developed&widely used (i.e, the Briggsian, since Napier's scheme was quite different, and haven't been used after him)

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Indeed.It seems more elegant, I guess.

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Char. Limit

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i think it should be [tex]\log_{a}(x)[/tex] with the default for missing [itex]a[/itex] to be [itex]a=e[/itex].

there is nothing wrong with [tex]log_{10}(x)[/tex] if that is what you want. and i never use log without an explicit base, unless it's base e.

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danago

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But seriously...

I agree that ln(x) is unambiguous for the natural log.

I think that log(x) is ALWAYS ambiguous, and that if you write log(x) the context should make it clear which one you mean, or you should write the base down. My impression is that this is accepted wisdom, and that it works well.

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btw: why would one want to use a log with 10 as a base? From what I have seen ln is almost always a good solution.

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You are right.btw: why would one want to use a log with 10 as a base? From what I have seen ln is almost always a good solution.

I suppose it's because the log function is easier to understand for those who have never worked with logarithms, if you use 10 as a base. So using 10 as a base could be a way to learn what the function means and learn about its properties. For those who know this well, it is recommended to let the base be e.

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Worrying about the logic is not all that common in math terms. I have met engineers who thought the term "imaginary numbers," was unfortunate, since they were as real as real numbers. For centuries, "Fermat’s Last Theorem," was simply a conjecture

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Historically, log X is to the base 10. That was how Briggs wrote the first log book in 1617. However, Napier in 1618 evidently recognized the natural log base. But e, Euler's number, was first written up in 1736.

Leibenz first wrote on the Calculus in 1675, before that time, I doubt there was much use to In X.

As for the logic of math terms, we have "The Method of Cardan." However, Cardan himself admitted to stealing the idea from Tartaglia. This could make some math teachers wary of the term, but as one professor put it, Cardan first published and that is where the credit belongs.

Leibenz first wrote on the Calculus in 1675, before that time, I doubt there was much use to In X.

As for the logic of math terms, we have "The Method of Cardan." However, Cardan himself admitted to stealing the idea from Tartaglia. This could make some math teachers wary of the term, but as one professor put it, Cardan first published and that is where the credit belongs.

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Base e: ln or log

Base 10: lg

Base 2: ld

Base a: log_a

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