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Math Help - Natural log equations question

  1. #1
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    Natural log equations question

    The equation 3lnx=lb3x is solved by the sqaure root of 3.

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  2. #2
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    Re: Natural log equations question

    3ln(x) = ln(3x)

    ln(x3) = ln(3x)

    x3 = 3x

    x3 - 3x = 0

    x (x2 - 3) = 0

    x = 0 or else x2 - 3 = 0
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    Re: Natural log equations question

    Edited...
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  4. #4
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    Re: Natural log equations question

    Quote Originally Posted by tom@ballooncalculus View Post
    3ln(x) = ln(3x)

    ln(x3) = ln(3x)

    x3 = 3x

    x3 - 3x = 0

    x (x2 - 3) = 0

    x = 0 or else x2 - 3 = 0
    Note that \displaystyle \begin{align*} x = 0 \end{align*} and \displaystyle \begin{align*} x = -\sqrt{3} \end{align*} are NOT acceptable solutions, because \displaystyle \begin{align*} \ln{x} \end{align*} is only defined for \displaystyle \begin{align*} x > 0 \end{align*}.
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