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Logarithmic equation

  1. Feb 20, 2007 #1
    1. The problem statement, all variables and given/known data
    I'm trying to solve this logarithmic equation, which has 3 possible solutions. However, I can only get to one of them. What are other ways I can solve it so I get to these other solutions?

    2. Relevant equations
    (ln x)^3 = 3 ln x

    3. The attempt at a solution
    (ln x)^3 = 3 ln x
    (ln x)^2 = 3
    ln x = sqrt(3)
    e^sqrt(3) = x
  2. jcsd
  3. Feb 20, 2007 #2


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    Staff Emeritus
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    MAke the substitution y=lnx. Then your equation becomes y3-3y=0. Can you solve this for y?

    (Note: You don't have to make the substitution; you could do it using your method. Your problems are:
    Here you lost a solution by dividing by lnx
    Here you only took one value of the square root)
    Last edited: Feb 20, 2007
  4. Feb 20, 2007 #3
    Thanks a lot.

    x = 1, e^sqrt(3), e^-sqrt(3)
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