If $\log_{3}2,\log_{3}\left( 2^{x} - 5 \right)$ and $\log_{3}\left( 2^{x} - \frac{7}{2} \right)$ are in arithmetic progression, determine the value of $x$ - Math Practice Question | divineJEE

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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 arithmetic progression, determine the value of $x$

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