If \( \log _{3} 2, \log _{3}\left(2^{x}-5\right) \) and \( \log _{3}\left(2^{x}-\frac{7}{2}\righ...

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If \( \log _{3} 2, \log _{3}\left(2^{x}-5\right) \) and \( \log _{3}\left(2^{x}-\frac{7}{2}\right) \) are in A.P., determine the value of \( x \).
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