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Homework Help: Log substitution problem

  1. Apr 25, 2007 #1
    1. The problem statement, all variables and given/known data

    (Idk how to put in the equation to make sense, therefore it is at the link below)

    2. Relevant equations



    3. The attempt at a solution

    Here is all I have done. Something just isn't right...there should be 3 answers (in the back of the book) because there is a cube involved...

    http://i123.photobucket.com/albums/o318/trashfile_bucket/Trash/2007-04-25-2009-26_edited.jpg
     
  2. jcsd
  3. Apr 25, 2007 #2

    mjsd

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    Homework Helper

    note:
    [tex](\log x)^3 \neq \log (x^3)[/tex] ie. 2nd step is wrong

    hint: a make substitution: y = log x and solve for y first then x.
     
  4. Apr 25, 2007 #3
    The first thing you've done is to cube both sides. That's ok but it should give you
    [tex] ( log(x) )^3 = log(x) [/tex]
    Since the whole log(x) is cubed, you can't move the 3 down (that's only if the x was cubed).

    But what you can do is take all the terms over to one side and then you just have to solve a cubic (which will give you 3 solutions). You may want to make it easier to see by introducing a new variable, [tex] u = log(x) [/tex] for example.
     
  5. Apr 25, 2007 #4
    Good to go!
     
  6. Apr 27, 2007 #5
    and the solutiions should probbably be, couse i just glanced at it,:
    x_1=1
    x_2=y,(if the base of the logarithm is y, couse i could not see it clear)
    x_3=1/y
     
    Last edited: Apr 27, 2007
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