Find the positive difference between the two real values of $x$ for which $$(\log_2 x)^4 + 12(\log_2(\frac{1}{x}))^2 - 2^6 = 0$$ A $4$ B $16$ C $\frac{15}{4}$ D $\frac{17}{4}$ E $\frac{255}{16}$ F $\frac{257}{16}$
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Find the positive difference between the two real values of $x$ for which
$$(\log_2 x)^4 + 12(\log_2(\frac{1}{x}))^2 - 2^6 = 0$$
A $4$
B $16$
C $\frac{15}{4}$
D $\frac{17}{4}$
E $\frac{255}{16}$
F $\frac{257}{16}$