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Math Help - [SOLVED] exponential e problem, solve for roots

  1. #1
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    [SOLVED] exponential e problem, solve for roots

    Hey all, I seem to be having some trouble finding the solutions (roots) to this equation:

    0=210-10(e^(x/30) + e^(-x/30))

    I got it down to this lol:

    21=e^(x/30) + e^(-x/30)

    and it seems like it should be easy, just I can't seem to simplify it down enough to be able to take the natural log from both sides

    Any help would be greatly appreciated,

    thanks!
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  2. #2
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    Quote Originally Posted by tkdiamond08 View Post
    Hey all, I seem to be having some trouble finding the solutions (roots) to this equation:

    0=210-10(e^(x/30) + e^(-x/30))

    I got it down to this lol:

    21=e^(x/30) + e^(-x/30)

    and it seems like it should be easy, just I can't seem to simplify it down enough to be able to take the natural log from both sides

    Any help would be greatly appreciated,

    thanks!
    Let w = e^{x/30}: 21 = w + \frac{1}{w}.

    Re-arrange this into a quadratic equation in w, solve for w and hence solve for x.
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  3. #3
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    Quote Originally Posted by tkdiamond08 View Post
    Hey all, I seem to be having some trouble finding the solutions (roots) to this equation:

    0=210-10(e^(x/30) + e^(-x/30))

    I got it down to this lol:

    21=e^(x/30) + e^(-x/30)

    and it seems like it should be easy, just I can't seem to simplify it down enough to be able to take the natural log from both sides

    Any help would be greatly appreciated,

    thanks!
    let u = \frac{x}{30}

    21 = e^u + e^{-u}

    multiply every term by e^u ...

    21e^u = e^{2u} + 1

    0 = (e^{u})^2 - 21e^u + 1

    quadratic formula ...

    e^u = \frac{21 \pm \sqrt{(-21)^2 - 4}}{2}

    e^u = \frac{21 \pm \sqrt{437}}{2}

    u = \ln\left(\frac{21 \pm \sqrt{437}}{2}\right)

    x = 30\ln\left(\frac{21 \pm \sqrt{437}}{2}\right)
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  4. #4
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    Thanks guys!

    Oh and sorry for initially posting it in the wrong forum.
    Last edited by mr fantastic; September 24th 2009 at 03:41 PM. Reason: Added the word 'initially'
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