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Question

If x = 1 +loga bc, y = 1 + logb ca, z = 1 + logc ab. Find the value of xy + yz + zx.


A

+ +

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B
xyz
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C

+ +

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D

1

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Solution

The correct option is B xyz
Given x = 1 + loga bc=logaa+logabc=logaabc
1x=logabca
Similarly 1y=logabcb,1z=logabcc
1x+1y+1z=logabca+logabcb+logabcc
=logabcabc=1
1x+1y+1z=1xy+yz+zx=xyz

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