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Math Help - solve for X

  1. #1
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    solve for X

    Solve for X: e^x(6-e^X)=9
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by VNVeteran View Post
    Solve for X: e^x(6-e^X)=9
    Distributing and rearranging, we get e^{2x}-6e^x+9=0.

    Do you notice anything nice about this expression (don't think too hard about it)?
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  3. #3
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    From where Chris left off consider a substitution

    a = e^x

    giving

    a^{2}-6a+9=0

    Now you only need to solve a qudartic
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  4. #4
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    Quote Originally Posted by pickslides View Post
    From where Chris left off consider a substitution

    a = e^x

    giving

    a^{2}-6a+9=0

    Now you only need to solve a qudartic
    (a-3) (a-3)
    a=3 a=3
    now what?
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  5. #5
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by VNVeteran View Post
    (a-3) (a-3)
    a=3 a=3
    now what?
    a=e^x, so e^x=3\implies x=\ldots
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  6. #6
    Super Member bigwave's Avatar
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    it factors to
    <br />
(e^x - 3)(e^x - 3)

    e^x = 3

    take ln to both sides

    lne^x = ln3

    lne cancels out

    so you have x = ln3
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