The solution set of the equation \( \log _{x} 2 \log _{2 x} 2=\log _{4 x} 2 \) is....

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The solution set of the equation
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\( \log _{x} 2 \log _{2 x} 2=\log _{4 x} 2 \) is
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(1) \( \left\{2^{-\sqrt{2}}, 2^{\sqrt{2}}\right\} \)
(2) \( \left\{\frac{1}{2}, 2\right\} \)
(3) \( \left\{\frac{1}{4}, 4\right\} \)
(4) \( \left\{\frac{1}{8}, 8\right\} \)


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