Answer
$\frac{1}{4}, 4$
Work Step by Step
1. $log_2x^{log_2x}=4 \Longrightarrow (log_2x)^2=4 \Longrightarrow log_2x=\pm2 \Longrightarrow x= \frac{1}{4}, 4$
2. Check, $x= \frac{1}{4}, 4$ fit(s).
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