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Math Help - Solve e^(2x) - e^x - 6 = 0 for x. Can't seem to set this up correctly!

  1. #1
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    Solve e^(2x) - e^x - 6 = 0 for x. Can't seem to set this up correctly!

    I need help setting up this properly... Solve e^(2x) - e^x - 6 = 0 for x.

    I keep running into dead ends! Do I need to make some sort of substitution? Please help, I'd really appreciate it!
    Last edited by mr fantastic; May 27th 2010 at 07:41 PM. Reason: Copied equation from post title.
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  2. #2
    Senior Member AllanCuz's Avatar
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    Quote Originally Posted by ktehspynx View Post
    I need help setting up this properly... I keep running into dead ends! Do I need to make some sort of substitution? Please help, I'd really appreciate it!
     e^{2x} - e^x - 6 = 0

     e^{x} e^x - e^x - 6 = 0

    This looks like a quadratic equation to me

    Let  e^x = u

     u^2 - u - 6 = 0

     (u-3)(u+2) = 0

    It follows that,

     e^x = 3 and  e^x = -2

    But since the negative root produces imaginary values, we will leave it

    Take,

     e^x = 3

    x = ln3
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  3. #3
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    Ah, I see it now! Thanks so much.
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