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Thread: logarithmic equation

  1. #1
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    logarithmic equation

    Solve for all real values of x:


    log_2{\bigg(x^{log_2x}\bigg)} \ = \ 4




    (The first "2" that you see on the farther left is supposed to be in a subscript position and act as base 2 for the logarithm.)
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  2. #2
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    Re: logarithmic equation

    $\log_2(x^{\log_2(x)})=4$

    $x^{\log_2(x)} = 16$

    $2^{(\log_2(x))^2} = 16$

    $\left(\log_2(x)\right)^2 = 4$

    $\log_2(x) = \pm 2$

    $x = 2^{\pm 2} = \dfrac 1 4,~4$
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  3. #3
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    Re: logarithmic equation

    Quote Originally Posted by greg1313 View Post
    Solve for all real values of x:
    log_2{\bigg(x^{log_2x}\bigg)} \ = \ 4
    Another way: log_2{\bigg(x^{log_2x}\bigg)} = \left(\log_2(x)\right)^2
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