If ${\log _e}\left( {{{a + b} \over 2}} \right) = {1 \over 2}({\log _e}a + {\log _e}b)$, then relation between $a$ and $b$ will be

  • A

    $a = b$

  • B

    $a = {b \over 2}$

  • C

    $a =2 b$

  • D

    $a = {b \over 3}$

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