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Math Help - Using natural logs to solve for x

  1. #1
    Rae
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    Using natural logs to solve for x

    Solve for x: 3e^(-x) = 4^(3x-1)


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  2. #2
    MHF Contributor harish21's Avatar
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    3e^{(-x)} = 4^{(3x-1)}

    \dfrac{3}{e^x}=4^{3x-1}

    3 = e^{(x)}\cdot 4^{3x-1}

    take log on both sides:

    \log{(3)} = \log\bigg(e^{(x)}\cdot 4^{3x-1}\bigg)

    now use \log(AB)=\log(A)+\log(B) on the RHS.
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  3. #3
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    Or, more directly, take the logarithm of both sides of the original equation:
    ln(3e^{-x})= -x+ ln(3)= ln(4^{3x-1})= (3x-1)ln(4)

    Now you have -x+ ln(3)= 3ln(4)x- ln(4) which is a linear equation.
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