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Does ln[ln(x)] = ln(x) * ln(x)

  1. Jan 23, 2010 #1
    1. The problem statement, all variables and given/known data
    Does ln[ln(x) = ln(x) times ln(x)?


    2. Relevant equations


    3. The attempt at a solution
     
  2. jcsd
  3. Jan 23, 2010 #2

    Dick

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    Science Advisor
    Homework Helper

    Well, no. Take x=e. ln(e)*ln(e)=1, ln(ln(e))=ln(1)=0.
     
  4. Jan 23, 2010 #3

    Mark44

    Staff: Mentor

    And generally speaking, f(f(x)) is different from f(x)*f(x). It's the difference between function composition (evaluation a function of a function) and function multiplication.
     
  5. Jan 24, 2010 #4

    Mentallic

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    Homework Helper

    Maybe if we manipulated the expression a little it will become clearer that each function is not equal to each other.

    [tex]ln\left(ln(x)\right)=\left(ln(x)\right)^2[/tex]

    [tex]ln(x)=e^{\left(ln(x)\right)^2}[/tex]

    [tex]ln(x)=(e^{ln(x)})^{ln(x)}[/tex]

    [tex]ln(x)=x^{ln(x)}[/tex]

    Does it look more obvious now as to why these expressions are not equal?
     
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