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Question

For positive numbers x, y and z the numerical value of the determinant ∣∣ ∣ ∣∣1logxylogxzlogyx1logyzlogzxlogzy1∣∣ ∣ ∣∣ is

A
0
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B
1
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C
logexyz
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D
None of these
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Solution

The correct option is A 0
∣ ∣ ∣1logxylogxzlogyx1logyzlogzxlogzy1∣ ∣ ∣=(1logzylogyz)logxy(logyxlogzxlogyz)+logxz(logy x logz ylogz x)=(11)(1logx ylogy x)+(logx zlog2x1)=0
{Since logxy.logyx=1}.

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