A) \[0\]
B) \[1\]
C) \[3\]
D) none of these
Correct Answer: B
Solution :
Key Idea: By the properties of logarithm\[{{\log }_{a}}b\times {{\log }_{b}}c={{\log }_{a}}c\] Given that, \[x={{\log }_{b}}a,\,\,y={{\log }_{c}}b,\,\,z={{\log }_{a}}c\] \[\therefore \] \[xyz={{\log }_{b}}a\times {{\log }_{c}}b\times {{\log }_{a}}c\] \[={{\log }_{b}}a\times {{\log }_{a}}c\times {{\log }_{c}}b\] \[={{\log }_{b}}c\times {{\log }_{c}}b\] \[={{\log }_{b}}b=1\]
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