If $x$, $y$, and $z$ are distinct and $x \neq 0$, $x \neq 1$, $y \neq 0$, $y \neq 1$, $z \neq 0$, and $z \neq 1$, the value of $\begin{vmatrix} \log x & \log y & \log z \\ \log 2x & \log 2y & \log 2z \\ \log 3x & \log 3y & \log 3z \end{vmatrix}$ is equal to