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Question

# Suppose x,y,z >0 and are not equal to 1 and logx+logy+logz=0. What is the value of x1logy+1logz×y1logz+1logx×z1logx+1logy.(All log functions have base 10)

A
103
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B
104
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C
102
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D
none of these
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Solution

## The correct option is A 10−3Let, K=x1logy+1logz×y1logz+1logx×z1logx+1logyTaking log on both the sides,logK=logx[1logy+1logz]+logy[1logz+1logx]+logz[1logx+1logy]→(i) Putting logx+logy+logz=0 (given), we get logxlogy+logzlogy=−1;logylogx+logzlogx=−1;logxlogz+logylogz=−1∴ R.H.S. of Eq.(i)=−3 ⇒log10K=−3 or K=10−3

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