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Logarithmic Equation with x on both sides

  1. Oct 25, 2008 #1
    Exponential Equation with x on both sides

    1. The problem statement, all variables and given/known data

    18x^2=6e^(2x)

    2. Relevant equations
    I don't know any for the step I got stuck on.


    3. The attempt at a solution
    3x^2=e^2x
    ln3x^2=lne^2x
    2ln3x=2x
    ln3x=x
     
    Last edited: Oct 25, 2008
  2. jcsd
  3. Oct 25, 2008 #2

    Dick

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    Science Advisor
    Homework Helper

    Please start using more parentheses, ok? If you mean 3*x^2=e^(2x), then taking logs gives you log(3)+2*log(x)=2*x. The left side is not 2ln3x, whatever that means. You can't solve that using elementary functions. You can prove a solution exists, and you can solve it numerically, but that's about it.
     
  4. Oct 25, 2008 #3
    Thank you for your reply! And sorry about the lack of parenthesis.

    By solving it numerically, do you mean guess and checking values for x? Or actually solving for x?
     
  5. Oct 25, 2008 #4

    rock.freak667

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    Homework Helper

    Well yes you can guess values using the intermediate value theorem and show that a solution exists.
     
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