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Math Help - Natural logarithm equation

  1. #1
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    Natural logarithm equation

    Hello,

    How do I solve the following equation? \ln{(x-5)}+\ln{(x+16)} = \ln{(5)}

    I tried the following, but apparently this is not correct, i.e. score = 0%.

    \ln{(x-5)}+\ln{(x+16)} = \ln{(5)}
    \ln{((x-5)(x+16))} = \ln{(5)}
    (x-5)(x+16) = 5
    x^2+16x-5x-80 = 5
    x^2+11x-85 = 0
    D = b^2-4ac = 11^2-4*1*-85 = 121 - (-340) = 121+340 = 461
    x_1 = \frac{-b+\sqrt{D}}{2a} = \frac{-11+\sqrt{461}}{2}
    x_2 = \frac{-b-\sqrt{D}}{2a} = \frac{-11-\sqrt{461}}{2}
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  2. #2
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    Re: Natural logarithm equation

    What's the domain of log?
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  3. #3
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    Re: Natural logarithm equation

    Quote Originally Posted by JakeBarnes View Post
    What's the domain of log?
    I know \ln{(x)} is only defined for x > 0. So one of the answers should be correct, but the problem is none of them are...
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  4. #4
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    Re: Natural logarithm equation

    As we have ln(x-5) in the equation any solution must be >5
    So only your first answer applies.
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  5. #5
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    Re: Natural logarithm equation

    Quote Originally Posted by Lotte1990 View Post
    I know \ln{(x)} is only defined for x > 0. So one of the answers should be correct, but the problem is none of them are...
    Your first solution is correct.
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