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Math Help - Solve for X

  1. #1
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    Solve for X

    Solve for X

    X: E^(2x)-(5E^x)-6=0

    You don't have to solve it for me, but if I could get a hint it would help. Thanks ahead of time.
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  2. #2
    Senior Member BAdhi's Avatar
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    Re: Solve for X

    take
    e^x=y

    then y^2-5y-6=0 (a normal quadric equation)
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  3. #3
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    Re: Solve for X

    Thanks BAdhi.

    So I substitute and use the quadratic equation. And I get say Y=6 or Y=-1. Then I say E^x=6 or E^x=-1. Do I now say, Log e (6)=x, or log e (-1)=x

    And because log e (-1)=x, I can say that E must equal in this case=-1, and x must be an odd integer?

    So, X=all odd integers, or X=log e (6)? Depending on which solution for E you use? Is this correct, and if so how do I properly write this answer?
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  4. #4
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    Re: Solve for X

    Quote Originally Posted by StudentMCCS View Post
    Thanks BAdhi.

    So I substitute and use the quadratic equation. And I get say Y=6 or Y=-1. Then I say E^x=6 or E^x=-1. Do I now say, Log e (6)=x, or log e (-1)=x

    And because log e (-1)=x, I can say that E must equal in this case=-1, and x must be an odd integer?

    So, X=all odd integers, or X=log e (6)? Depending on which solution for E you use? Is this correct, and if so how do I properly write this answer?
    \displaystyle \ln{x} is only defined for \displaystyle x > 0...
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