If \log_{3}2,\log_{3}( 2^{x} - 5 ) and \log_{3}( 2^{x} - \frac{7}{2} ) are in arithmetic progression, determine the value of x: Sequence & Series (Mathematics)

\log_{3}2,\log_{3}\left( 2^{x} - 5 \right)

and

\log_{3}\left( 2^{x} - \frac{7}{2} \right)

are in arithmetic progression, determine the value of

x

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