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Ln(1+e^x)=2 Problem

  1. Apr 13, 2015 #1
    1. The problem statement, all variables and given/known data
    I have to solve ln(1+e^x)=2 for x

    2. Relevant equations


    3. The attempt at a solution
    ln(1+e^x)=2
    ln(1+e^x)=lne^2
    (1+e^x)=e^2
    e^x=e^2-1
    x=(e^2-1)

    The real answer is x=ln(e^2-1) but I dont understand why we have to put the ln back? why cant we keep it like that x=(e^2-1).

    thank you very much
     
    Last edited: Apr 13, 2015
  2. jcsd
  3. Apr 13, 2015 #2

    SammyS

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    That should be e^ln(1+e^x) = e^2

    Maybe it's a typo.
    Take the natural log of both sides !

     
  4. Apr 13, 2015 #3
    ln(1+e^x)=2
    ln(1+e^x)=lne^2 -- forgot to add the ln there.
    then I take out ln on both side then at the end I basically have to add ln back to reduce it to x?
     
  5. Apr 13, 2015 #4

    SammyS

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    The "both sides" refers to the following from your Original Post.
     
  6. Apr 13, 2015 #5
    OHH sorry my bad, thank you very much, I understand now :)
     
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