The value of the determinant \(\begin{vmatrix}\log_{2} 8 & \log_{3} 9\\ \log_{2} 4 & \log_{3} 27\end{vmatrix}\) is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 5
Each logarithm here is a whole number:
\(\log_{2} 8 = 3\) since \(2^{3} = 8\); \(\log_{3} 9 = 2\) since \(3^{2} = 9\)
\(\log_{2} 4 = 2\) since \(2^{2} = 4\); \(\log_{3} 27 = 3\) since \(3^{3} = 27\)
\(\displaystyle \begin{vmatrix}3 & 2\\ 2 & 3\end{vmatrix} = 3 \times 3 - 2 \times 2\)
\(= 9 - 4 = 5\)