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Math Help - simplifying logs

  1. #1
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    simplifying logs

    Solve the equation:




    Correct Answer: -6+7^(1/2)


    can someone explain how I would obtain the answer above? I know how to actually solve for x numerically, but I don't know how to get -6+7^(1/2)
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    Re: simplifying logs

    Start by simplifying the left hand side using the law of logarithms: log(x) + log(y) = log(xy)
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    Re: simplifying logs

    I get x^2+12x+29=0 but how to factor that since 29 is prime?
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    Re: simplifying logs

    Use the quadratic formula
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    Re: simplifying logs

    Just as a reminder:

    x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}
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    Re: simplifying logs

    Quote Originally Posted by kingsolomonsgrave View Post
    I get x^2+12x+29=0 but how to factor that since 29 is prime?
    complete the square ...

    x^2+12x = -29

    x^2 + 12x + 36 = 36-29

    (x + 6)^2 = 7

    x+6 = \pm \sqrt{7}

    x = -6 \pm \sqrt{7}

    since x > -4 ...

    x = -6 + \sqrt{7}
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