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  • Please solve RD Sharma class 12 chapter Determinants exercise multiple choise question 17 maths textbook solution

Please solve RD Sharma class 12 chapter Determinants exercise multiple choise question 17 maths textbook solution

Answers (1)

Answer:

Correct option (b)

Hint:

Use logarithm properties

Solution:

        \left|\begin{array}{cc} \log _{3}^{512} & \log _{4}^{3} \\ \log _{3}^{8} & \log _{4}^{9} \end{array}\right| \times\left|\begin{array}{ll} \log _{2}^{3} & \log _{8}^{3} \\ \log _{3}^{4} & \log _{3}^{4} \end{array}\right|

        =\left|\begin{array}{cc} \log _{3}{ }^{2^{9}} & \log _{4}^{3} \\ \log _{3}^{2^{3}} & \log _{4}^{3^{2}} \end{array}\right| \times\left|\begin{array}{cc} \log _{2}^{3} & \log _{8}^{3} \\ \log _{3}^{2^{2}} & \log _{3}^{2^{2}} \end{array}\right|

        =\left|\begin{array}{cc} 9\log _{3}{ }^{2} & \log _{4}^{3} \\ 3\log _{3}^{2} & 2\log _{4}^{3} \end{array}\right| \times\left|\begin{array}{cc} \log _{2}^{3} & \log _{8}^{3} \\ 2\log _{3}^{2} & 2\log _{3}^{2} \end{array}\right|

        =\left[\left(9 \times \frac{\log 2}{\log 3} \times 2 \times \frac{\log 3}{\log 4}\right)-3 \times \frac{\log 2}{\log 3} \times \frac{\log 3}{\log 4}\right] \times\left[\frac{\log 3}{\log 2} \times 2 \times \frac{\log 2}{\log 3}-\frac{\log 3}{\log 8} \times 2 \times \frac{\log 2}{\log 3}\right]

        =\left(18 \times \frac{\log 2}{2 \log 2}-3 \times \frac{\log 2}{2 \log 2}\right)\left(2-2 \times \frac{1}{3 \log 2} \times \log 2\right)

        =(9-\frac{3}{2})(2-\frac{2}{3})

        =\frac{15}{2}\times \frac{4}{3}

        =10

Posted by

Gurleen Kaur

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