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Question-10774




Question Number 10774 by j.masanja06@gmail.com last updated on 24/Feb/17
Answered by sandy_suhendra last updated on 24/Feb/17
= determinant (((log_3 1024    1)),((log_3 8            2)))× determinant (((log_2 3    log_4 3)),((log_3 4    log_3 4)))  =(2log_3 1024−log_3 8)×(log_2 3.log_3 4−log_4 3.log_3 4)      =(log_3 ((1024^2 )/8))×(log_2 4−1)  =(log_3 2^(17) )×(2−1) = 17 log_3 2
$$=\begin{vmatrix}{\mathrm{log}_{\mathrm{3}} \mathrm{1024}\:\:\:\:\mathrm{1}}\\{\mathrm{log}_{\mathrm{3}} \mathrm{8}\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{2}}\end{vmatrix}×\begin{vmatrix}{\mathrm{log}_{\mathrm{2}} \mathrm{3}\:\:\:\:\mathrm{log}_{\mathrm{4}} \mathrm{3}}\\{\mathrm{log}_{\mathrm{3}} \mathrm{4}\:\:\:\:\mathrm{log}_{\mathrm{3}} \mathrm{4}}\end{vmatrix} \\ $$$$=\left(\mathrm{2log}_{\mathrm{3}} \mathrm{1024}−\mathrm{log}_{\mathrm{3}} \mathrm{8}\right)×\left(\mathrm{log}_{\mathrm{2}} \mathrm{3}.\mathrm{log}_{\mathrm{3}} \mathrm{4}−\mathrm{log}_{\mathrm{4}} \mathrm{3}.\mathrm{log}_{\mathrm{3}} \mathrm{4}\right)\:\:\:\: \\ $$$$=\left(\mathrm{log}_{\mathrm{3}} \frac{\mathrm{1024}^{\mathrm{2}} }{\mathrm{8}}\right)×\left(\mathrm{log}_{\mathrm{2}} \mathrm{4}−\mathrm{1}\right) \\ $$$$=\left(\mathrm{log}_{\mathrm{3}} \mathrm{2}^{\mathrm{17}} \right)×\left(\mathrm{2}−\mathrm{1}\right)\:=\:\mathrm{17}\:\mathrm{log}_{\mathrm{3}} \mathrm{2} \\ $$

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