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Rewriting the function e^-x*x^t-1

  1. Dec 8, 2013 #1
    does e^-x*x^(t-1)=
    e^(t*ln(x)-ln(x)-x)
    heres my reasoning:
    x=e^ln(x)
    e^-x*x^(t-1)=
    e^-x*e^(ln(x)(t-1))=
    e^-x*e^(t*ln(x)-ln(x))=
    e^(t*ln(x)-ln(x)-x)

    I want it in the latter form so that it is easier to take derivatives and antiderivatives. did i make any mistakes?
     
    Last edited: Dec 8, 2013
  2. jcsd
  3. Dec 8, 2013 #2

    D H

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    Where are your parentheses? As written, your expression is ##e^{-x}x^t-1 = e^t \ln x - \lnx -x##, which obviously isn't true.
     
  4. Dec 8, 2013 #3
    youre right srry
     
  5. Dec 10, 2013 #4

    HallsofIvy

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    If you mean [itex]e^{-x}x^{t-1}[/itex] then it is equal to [itex]e^{-x}e^{ln(x^{t-1})}=[/itex][itex] e^{-x}e^{(t- 1)ln(x)} = e^{-x+ tln(x)- ln(x)}[/itex]
     
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