Question

\log_{3}512 & \log_{4}3 \\ \log_{3}8 & \log_{4}9 \end{matrix} \right| \times \left| \begin{matrix} \log_{2}3 & \log_{8}3 \\ \log_{3}4 & \log_{3}4 \end{matrix} \right| =$$

• A. 7
• B. 10
• C. 13
• D. 17

Answer 1

Answer: (B)

10

Answer 2

\log_{3}512 & \log_{4}3 \\ \log_{3}8 & \log_{4}9 \end{matrix} \right| \times \left| \begin{matrix} \log_{2}3 & \log_{8}3 \\ \log_{3}4 & \log_{3}4 \end{matrix} \right| = \left( \frac{\log 512}{\log 3} \times \frac{\log 9}{\log 4} - \frac{\log 3}{\log 4} \times \frac{\log 8}{\log 3} \right) \times \left( \frac{\log 3}{\log 2} \times \frac{\log 4}{\log 3} - \frac{\log 3}{\log 8} \times \frac{\log 4}{\log 3} \right) = \left( \frac{\log 2^{9}}{\log 3} \times \frac{\log 3^{2}}{\log 2^{2}} - \frac{\log 2^{3}}{\log 2^{2}} \right) \times \left( \frac{\log 2^{2}}{\log 3} - \frac{\log 2^{2}}{\log 2^{3}} \right) = \left( \frac{9 \times 2}{2} - \frac{3}{2} \right)\left( 2 - \frac{2}{3} \right) = 10$$