If \( x^{2 a} y^{3 b}=e^{5 m}, x^{3 c} y^{4 d}=e^{2 n}, \Delta_{1}=\left|\begin{array}{cc}5 m & ...
If \( x^{2 a} y^{3 b}=e^{5 m}, x^{3 c} y^{4 d}=e^{2 n}, \Delta_{1}=\left|\begin{array}{cc}5 m & 3 b \\ 2 n & 4 d\end{array}\right| \),
\( \Delta_{2}=\left|\begin{array}{cc}2 a & 5 m \\ 3 c & 2 n\end{array}\right|, \Delta_{3}=\left|\begin{array}{cc}2 a & 3 b \\ 3 c & 4 d\end{array}\right| \), then the values of \( x \) and are
(a) \( \frac{\Delta_{1}}{\Delta_{3}}, \frac{\Delta_{2}}{\Delta_{3}} \)
(b) \( \frac{\Delta_{2}}{\Delta_{1}}, \frac{\Delta_{3}}{\Delta_{1}} \)
(c) \( \log \left(\frac{\Delta_{1}}{\Delta_{3}}\right), \log \left(\frac{\Delta_{2}}{\Delta_{3}}\right) \)
(d) \( e^{\frac{\Delta_{1}}{\Delta_{3}}}, e^{\frac{\Delta_{2}}{\Delta_{3}}} \)
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