ISI2015-DCG-22

Question

The value of $$\begin{vmatrix} 1 & \log _x y & \log_x z \\ \log _y x & 1 & \log_y z \\ \log _z x & \log _z y & 1 \end{vmatrix}$$ is

• A. $0$
• B. $1$
• C. $-1$
• D. None of these

Answer 1

First row: logx/logx , logy/logx , logz/logx. Take 1/logx out then frist row will be logx , logy, logz

Similarly second and third row will become logx , logy . logz.

As two rows are identical, so determinant =0

Answer 2

Put x=y=z so answer is ZERO

Answer 3

anyway  solve you get answer = 0 which is option A