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Small confusion regarding logarithmic formula

  1. Jan 29, 2015 #1
    I've a small confusion about formula
    ##\log^3 n = \log \log \log n##
    or ##\log^3 n = (\log n)^3 ##
  2. jcsd
  3. Jan 29, 2015 #2

    Doc Al

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    Staff: Mentor

    That's the one you want.
  4. Jan 29, 2015 #3


    Staff: Mentor

    In exactly the same way, cos2(x) does not mean cos(cos(x)), but rather it means cos(x) * cos(x) = (cos(x))2. The exponent indicates repeated multiplication, not repeated function composition.
  5. Jan 29, 2015 #4


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    Science Advisor

    It is not uncommon to put a an exponent in parentheses to indicate a repeated composition.
    That is, [itex](log(x))^{(3)}[/itex] or [itex]log^{(3)}(x)[/itex] is "log(log(log(x)))".

    Unfortunately, that is also often used to indicate the third derivative so you must be careful to state which!
    Last edited by a moderator: Jan 30, 2015
  6. Jan 31, 2015 #5
    You mean ##\log^{(3)} n = (\log n)^{(3)} = \log (\log(\log n))##
    ##\log^3 n = (\log n)^3##
  7. Jan 31, 2015 #6


    Staff: Mentor

    The above is what HallsOfIvy said. I haven't seen it, myself, but I have seen f(3), with parentheses around the exponent, to indicate the third derivative.
    This is what I said.
  8. Jan 31, 2015 #7
    I know, I was just rechecking from you. :)
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