Question

5. Решите систему уравнений:
$\left \{ log_{4}x+ log_{4} {y=2} \atop 3^{xy+y-14} {=81}} \right.$

Answer 1

$\left \{ {{log_4x+log_4y=2} \atop {3^{xy+y-14}=81}} \right. \; \left \{ {{log_4(xy)=log_4(4^2)} \atop {3^{xy+y-14}=3^4}} \right. \; \left \{ {{xy=16} \atop {xy+y-14=4}} \right. \; \left \{ {{xy=16} \atop {16+y-14=4}} \right. \\\\ \left \{ {{xy=16} \atop {y=2}} \right. \; \left \{ {{2x=16} \atop {y=2}} \right. \; \left \{ {{x=8} \atop {y=2}} \right.$

$ODZ:\; x\ \textgreater \ 0,\; y\ \textgreater \ 0$