Let \( z(\neq 2) \) be a complex number such that \( \log _{1 / 2}|z-2| \) \( \log _{1 / 2}|z| \...

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Let \( z(\neq 2) \) be a complex number such that \( \log _{1 / 2}|z-2| \) \( \log _{1 / 2}|z| \). Then prove that \( \operatorname{Re}(z)1 \).
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