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Math Help - How to solve this simple exponential equation?

  1. #1
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    How to solve this simple exponential equation?

    (16e^x) - (16e^2x) = 3


    and the answer says that x = 0.25 but i can't see how you can get there? please help, much appreciated!! thanks!
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  2. #2
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    Rewrite it as \displaystyle 0 = 16e^{2x} - 16e^x + 3

    \displaystyle 0 = 16\left(e^x\right)^2 - 16e^x + 3.

    Now let \displaystyle X = e^x so that the equation becomes

    \displaystyle 0 = 16X^2 - 16X + 3, which is a quadratic equation you can solve for \displaystyle X, and then solve for \displaystyle x.
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  3. #3
    MHF Contributor FernandoRevilla's Avatar
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    Quote Originally Posted by Yehia View Post
    (16e^x) - (16e^2x) = 3 and the answer says that x = 0.25 but i can't see how you can get there? please help, much appreciated!! thanks!

    Have you correctly quoted the problem?
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  4. #4
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    Quote Originally Posted by Prove It View Post
    Rewrite it as \displaystyle 0 = 16e^{2x} - 16e^x + 3

    \displaystyle 0 = 16\left(e^x\right)^2 - 16e^x + 3.

    Now let \displaystyle X = e^x so that the equation becomes

    \displaystyle 0 = 16X^2 - 16X + 3, which is a quadratic equation you can solve for \displaystyle X, and then solve for \displaystyle x.
    thanks
    Last edited by Yehia; February 25th 2011 at 05:21 AM.
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  5. #5
    MHF Contributor FernandoRevilla's Avatar
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    Quote Originally Posted by Yehia View Post
    (16e^x) - (16e^2x) = 3 and the answer says that x = 0.25 but i can't see how you can get there? please help, much appreciated!! thanks!

    Thank you very much for answering to my previous question. Please, post your work if you get some of this

    (i) x=0,25 is a solution of the given equation.

    (ii) The equation has only one solution.
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