If $ \log _{3} 2, \log _{3}\left(2^{x}-5\right), \log _{3}\left(2^{x}-\frac{7} { 2}\right) $ are in A.P., then $ x $ is equal to [JEE Main 2021, 27 Jul (Shift 1)]

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If \( \log _{3} 2, \log _{3}\left(2^{x}-5\right), \log _{3}\left(2^{x}-\frac{7} { 2}\right) \) are in A.P., then \( x \)…

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