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Question

If x>0 and 1,y>0 and 1,z>0 and 1 then the value of
∣ ∣ ∣1logxylogxzlogyx1logyzlogzxlogzy1∣ ∣ ∣ is

A
0
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B
1
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C
1
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D
none of these
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Solution

The correct option is B 0
∣ ∣ ∣1logxylogxzlogyx1logyzlogzxlogzy1∣ ∣ ∣
=∣ ∣ ∣ ∣ ∣ ∣ ∣1logeylogexlogezlogexlogexlogey1logezlogeylogexlogezlogeylogez1∣ ∣ ∣ ∣ ∣ ∣ ∣
=1logexlogeylogez∣ ∣ ∣logexlogeylogezlogexlogeylogezlogexlogeylogez∣ ∣ ∣
=∣ ∣111111111∣ ∣
=0

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