Ans: (C)
\(\left|\begin{array}{lll}\frac{\log x}{\log x} & \frac{\log y}{\log x} & \frac{\log z}{\log x} \\ \frac{\log y}{\log y} & \frac{\log z}{\log y} \\ \mid \frac{\log x}{\log z} & \frac{\log y}{\log z} & \frac{\log z}{\log z}\end{array}\right|\)
Taking \(\frac{1}{\log x}, \frac{1}{\log y}, \frac{1}{\log z}\) common from \(R_{1}, R_{2}, R_{3}\) all rows are identical. So \(\Delta=0\)