If x, y, z are not equal and neq 0, neq 1,the | vedclass

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(C) Given the determinant $D = \begin{vmatrix} \log x & \log y & \log z \ \log 2x & \log 2y & \log 2z \ \log 3x & \log 3y & \log 3z \end{vmatrix}$.U

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(C) Given the determinant $D = \begin{vmatrix} \log x & \log y & \log z \ \log 2x & \log 2y & \log 2z \ \log 3x & \log 3y & \log 3z \end{vmatrix}$.Using the property $\log(ab) = \log a + \log b$,we can rewrite the rows:$R_2 ightarrow R_2 - R_1$ gives $\log 2x - \log x = \log 2$ for each element in the row.$R_3 ightarrow R_3 - R_1$ gives $\log 3x - \log x = \log 3$ for each element in the row.Thus,the determinant becomes:$D = \begin{vmatrix} \log x & \log y & \log z \ \log 2 & \log 2 & \log 2 \ \log 3 & \log 3 & \log 3 \end{vmatrix}$.Factoring out $\log 2$ from $R_2$ and $\log 3$ from $R_3$:$D = (\log 2)(\log 3) \begin{vmatrix} \log x & \log y & \log z \ 1 & 1 & 1 \ 1 & 1 & 1 \end{vmatrix}$.Since $R_2$ and $R_3$ are identical,the value of the determinant is $0$.

If $x, y, z$ are not equal and $\neq 0, \neq 1$,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

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