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Math Help - Unknown indice using logarithms

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    Unknown indice using logarithms

    Please help me with this logarithm equation:



    Thanks - solve in terms of x.
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    Quote Originally Posted by BG5965 View Post
    Please help me with this logarithm equation:



    Thanks - solve in terms of x.
    \log_2\left(2^{2x}-56\right) - x=0~\implies~\log_2\left(2^{2x}-56\right) = x

    Now use the base 2 with both sides of the equation:

    2^{2x}-56 = 2^x

    Use substitution 2^x = y that means y > 0.

    You'll get:

    y^2-y-56 = 0~\implies~y = -7~\vee~y=8

    You only can use the second solution:

    8=2^x~\implies~x=3
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