$l o g_{4} x^{2} = l o g_{4} x$

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Solution

We have,
$l o g_{4} x^{2} = l o g_{4} x$
$x^{2} = x$
$x^{2} - x = 0$
$x (x - 1) = 0$
$x = 0, 1$

Hence, this is the answer.

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