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Math Help - sorry, still part of the same qn

  1. #1
    Member maybeline9216's Avatar
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    sorry, still part of the same qn

    3 = 3 e^{\ln \left(1/\sqrt{3}\right)} + e^{\ln \sqrt{3}} = \frac{3}{\sqrt{3}} + \sqrt{3} = 2 \sqrt{3}

    How do u get this?
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  2. #2
    MHF Contributor
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    Quote Originally Posted by maybeline9216 View Post
    3 = 3 e^{\ln \left(1/\sqrt{3}\right)} + e^{\ln \sqrt{3}} = \frac{3}{\sqrt{3}} + \sqrt{3} = 2 \sqrt{3}

    How do u get this?
    The LHS must be y, not 3.

    e^[ln(y)] = y
    e^[ln(1/3)] = 1/3
    So,
    e^[ln(1/sqrt(3))] = 1/sqrt(3)

    Thus,
    y = 3/sqrt(3) +sqrt(3)
    y = sqrt(3) +sqrt(3)
    y = 2sqrt(3)
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