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If x=1+log(a) bc, y=1+log(b) ca, z=1+log...

If `x=1+log_(a) bc, y=1+log_(b) ca, z=1+log_(c) ab`, then `(xyz)/(xy+yz+zx)` is equal to

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The correct Answer is:
1
`x=log_(a) a+log_(a) bc=log_(a) abc`
Similarly `y=log_(b) abc`
`z=log_(c) abc`
`(xyz)/(xy+yz+zx)=1/(1/x+1/y+1/z)=1/(log_(abc) abc)=1`
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