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If $ae^{x}+be^{y}=c; pe^{x}+qe^{y}=d $ and $\bigtriangleup_{1}=\begin{vmatrix} a&b \\p&q \end{vmatrix}; \bigtriangleup_{2}=\begin{vmatrix} c&b\\d&q \end{vmatrix}; \bigtriangleup_{3}=\begin{vmatrix} a&c\\p&d \end{vmatrix}$ than the value of $(x , y )$ is

 \[\begin{array} {1 1}(1)\begin{pmatrix} \large\frac{\bigtriangleup_{2}}{\bigtriangleup_{1}},\frac{\bigtriangleup_{3}}{\bigtriangleup_{1}}\end{pmatrix}&(2)\begin{pmatrix}\log \large\frac{\bigtriangleup_{2}}{\bigtriangleup_{1}},\log\frac{\bigtriangleup_{3}}{\bigtriangleup_{1}}\end{pmatrix}\\(3)\begin{pmatrix}\log \large\frac{\bigtriangleup_{1}}{\bigtriangleup_{3}},\log\frac{\bigtriangleup_{1}}{\bigtriangleup_{2}}\end{pmatrix}&(4)\begin{pmatrix}\log \large\frac{\bigtriangleup_{1}}{\bigtriangleup_{2}},\log\frac{\bigtriangleup_{1}}{\bigtriangleup_{3}}\end{pmatrix}\end{array}\]

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