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Logarithm notation question

  1. Aug 20, 2011 #1
    1. The problem statement, all variables and given/known data
    is ln(x)3 the same as saying [ln(x)]3? Also, if there is a difference, which one applies to the exponent being moved into the front of the logarithm as in 3ln(x)?


    2. Relevant equations
    natural logarithms


    3. The attempt at a solution
    I just got tripped up on the notation. Normally I see logarithms written as ln(x)3, but when I saw this, I wasn't quite sure if it was the same or not. I wasn't too sure if it was like sin2(x) and [sin(x)]2.
     
  2. jcsd
  3. Aug 20, 2011 #2

    HallsofIvy

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    Yes, [itex]ln(x)^3[/itex] means [itex](ln(x))^3[/itex] as opposed to [itex]ln(x^3)[/itex]. (The second form, with parentheses, is preferable as it is clearer.) It is the latter to which we can apply the "law of logarithms": [itex]ln(x^3)= 3ln(x)[/itex].

    Look at a numerical example: ln(2)= 0.6931, approximately, so [itex](ln(2))^3= 0.3330[/itex] while [itex]ln(2^3)= ln(8)= 2.0794= 3ln(2)[/itex].
     
    Last edited: Aug 24, 2011
  4. Aug 24, 2011 #3
    Ah, thank you for the great explanation.
     
  5. Aug 24, 2011 #4

    uart

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    Be aware that you'll also see abbreviated notations without the brackets. Like,

    [tex]\log x^2 = \log(x^2)[/tex]

    and

    [tex]\log^2 x = ( \log(x) )^2[/tex]

    This type of notation is frequently used with trig functions too.
     
  6. Aug 26, 2011 #5
    ah thank you for further clarifying!
     
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