If ${\log _3}2,\;{\log _3}({2^x} - 5)$ and ${\log _3}\left( {{2^x} - \frac{7}{2}} \right)$ are in $A.P.$, then $x$ is equal to

  • [IIT 1990]
  • A

    $1,\;\frac{1}{2}$

  • B

    $1,\;\frac{1}{3}$

  • C

    $1,\;\frac{3}{2}$

  • D

    None of these

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