Logarithmic AP

Calculus Level 3

If \( \log _{ 3 }{ 2 } ,\log _{ 3 }{ ({ 2 }^{ x } } -5)\quad and\quad \log _{ 3 }{ ({ 2 }^{ x }-\frac { 7 }{ 2 } ) } \) are in AP, find \(x\)

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