The value of $\begin{vmatrix}\log_510&2\\2&\log_{10}5\end{vmatrix}$ is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → -3
Determinant = $\begin{vmatrix} \log_{5}{10} & 2 \\ 2 & \log_{10}{5} \end{vmatrix}$
Determinant $= \log_{5}{10}\cdot \log_{10}{5} - (2\cdot 2)$
Since $\log_{a}{b}=\frac{1}{\log_{b}{a}}$, we have $\log_{5}{10}=\frac{1}{\log_{10}{5}}$
So, $\log_{5}{10}\cdot \log_{10}{5} = 1$
Thus, Determinant $= 1 - 4 = -3$