Question

If $x,y,z$ are not equal and $\ne 0,\ne 1$ the value of $\left|\begin{array}{ccc}\log x& \log y& \log z\\ \log 2x& \log 2y& \log 2z\\ \log 3x& \log 3y& \log 3z\end{array}\right|$ is equal to

• A. $\log \left(xyz\right)$
• B. $\log \left(6xyz\right)$
• C. $0$
• D. $\log (x+y+z)$

Answer 1

The correct option is C $0$

$R_2\to R_2-R_1,R_3\to R_3-R_1$
$\Rightarrow \left|\begin{array}{ccc}\log x& \log y& \log z\\ \log 2& \log 2& \log 2\\ \log 3& \log 3& \log 3\end{array}\right|$
$=\log 2\log 3\left|\begin{array}{ccc}\log x& \log y& \log z\\ 1& 1& 1\\ 1& 1& 1\end{array}\right|=0$