If $x = {\log _a}(bc),y = {\log _b}(ca),z = {\log _c}(ab),$then which of the following is equal to $1$

  • A

    $x + y + z$

  • B

    ${(1 + x)^{ - 1}} + {(1 + y)^{ - 1}} + {(1 + z)^{ - 1}}$

  • C

    $xyz$

  • D

    None of these

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  • [IIT 2000]