A) -1
B) 0
C) 1
D) xyz
Correct Answer: C
Solution :
(c): \[x={{y}^{x}},y={{z}^{y}},z={{x}^{y}}\] \[\Rightarrow x=lo{{g}_{y}}x,y={{\log }_{z}}y,z={{\log }_{x}}z\] \[\Rightarrow xyz=\left( lo{{g}_{y}}x \right)\times \left( lo{{g}_{z}}y \right)\times \left( lo{{g}_{x}}z \right)\] \[\Rightarrow xyz=\left( \frac{\log x}{\log y}\times \frac{\log y}{\log z}\times \frac{\log z}{\log x} \right)=1.\]
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