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Math Help - simple logs

  1. #1
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    simple logs

    Hello there,

    Im a little stuck on this:

    e^2x + e^x - 2 = 0

    it says hint use e^2x = ((e^x)^2)

    im meant to get 0 but i get 0.23...
    can you help?
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  2. #2
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    Quote Originally Posted by darksupernova View Post
    Hello there,

    Im a little stuck on this:

    e^2x + e^x - 2 = 0

    it says hint use e^2x = ((e^x)^2)

    im meant to get 0 but i get 0.23...
    can you help?
    e^{2x} + e^x - 2 = 0

    (e^x)^2 + e^x - 2 = 0.

    You have a quadratic equation in e^x. So let X = e^x so that the equation looks like

    X^2 + X - 2 = 0

    (X + 2)(X - 1) = 0

    So X = -2 or X = 1.


    Therefore e^x = -2 or e^x = 1.

    But since e^x > 0 for all x, that means that only the second case is possible.


    So e^x = 1

    x = \ln{1}

    x = 0.
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  3. #3
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    i didnt spot that! Thanks very much!
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