A) \[x=y=z\]
B) \[x=4\]
C) \[x,\ y,\,z\] are in G.P.
D) All the above
Correct Answer: D
Solution :
\[{{\log }_{x}}y,\ {{\log }_{z}}x,\ {{\log }_{y}}z\] are in G.P. \[\Rightarrow \]\[{{({{\log }_{z}}x)}^{2}}={{\log }_{x}}y\times {{\log }_{y}}z={{\log }_{x}}z=\frac{1}{{{\log }_{z}}x}\] \[\Rightarrow \]\[{{({{\log }_{z}}x)}^{3}}=1\]\[\Rightarrow \]\[z=x\] Also, we can show \[z=x=y=4\].
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