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What is log (100) ?

  1. 4.60517

    1 vote(s)
  2. 2

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  1. Sep 13, 2013 #1
    Without trying to lean anyone to either answer, I will post WHY I asked this question after I gather some data from the poll. thanks. Pretty simple question:

    What is log (100) ?

    If you can, please post what degree you have and what field, for example:
    Bachelor of Engineering: Civil

  2. jcsd
  3. Sep 13, 2013 #2


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    Gold Member

    Your question is meaningless without specifying what base you are using. I assume that's your point but it's not a very interesting one.
  4. Sep 13, 2013 #3
    You should just write what you are thinking. Historically, log has meant natural log. Nowadays, its means log base 10. This is the case in early math education more than it is in research and higher science where log can still mean the natural log. Usually with the context its quite clear (sometimes, the difference doesn't matter at all). If you are in college algebra log means base 10. If you are using a calculator log means base 10. If you are viewing Boltzmann's tombstone log means base e.
  5. Sep 13, 2013 #4


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    Science Advisor

    When doing arithmetic using logs, base 10 is used. When doing calculus, base e is used. To distinguish sometimes base 10 is written log, while base e is written ln.
  6. Sep 13, 2013 #5
    Neither. Typically, out of habit, I use ##\log## to mean the base 10 logarithm. I've been meaning to break this habit ever since micromass told me that it was more agreeable with modern notation to use ##\log## for the natural logarithm. Now is as good a time as ever to do so, I guess.

    ##\log(100)=\operatorname{Log}(100)+2\pi i n##, where ##\operatorname{Log}## is the principle value of the natural logarithm and ##n\in\mathbb{Z}##.

    Your use of the word "is" along with the truncation of the decimal expansion of ##\operatorname{Log}(100)## disturbs me.

    Remember that we define ##\log## as the inverse of exponentiation. Thus, if ##e^x=y##, then ##\log(y)=x##. Observe: $$e^t=e^t\cdot 1 \\ e^t=e^te^{2\pi i n}\quad (n\in\mathbb{Z}) \\ e^t=e^{t+2\pi i n} \\ \log(x)=t+2\pi i n \quad (\text{Here we have made the substitution } x=e^t).$$ We might even define, from this case, ##\operatorname{Log}(x)=t##. The point of this is that the natural logarithm is NOT a function from complex numbers to complex numbers. Instead, it is multivalued (unless we define it on something called a Riemann surface).
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