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Math Help - A somewhat simple equation

  1. #1
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    A somewhat simple equation

    I just got stuck and is without tutoring for the weekend, I found this forum after some searching on the net and hope to find help here.

    Can anyone solve:
    e^x-e^{-x}=6 or if you wish sineh(x)=3?

    Edit: Maybe I should add, it's not an answer I am looking for more like a solution or maybe a hint.
    Last edited by MathGuru; October 6th 2005 at 02:32 PM. Reason: add latex
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  2. #2
    hpe
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    Quote Originally Posted by a4swe
    Can anyone solve:
    e^x-e^{-x}=6 or if you wish sineh(x)=3?
    Set z = e^x and thus e^{-x} = \frac{1}{z}. Then your equation becomes
     z - \frac{1}{z}  = 6 or  z^2 - 1 = 6z.
    This is a quadratic equation that you can solve with the usual methods. Then solve for x. Works for all equations of the form \cosh x = a or \sinh x = a.
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  3. #3
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    Thank you for a perfect answer.
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