Question

Вот система уравнений логарифмов, нужна помощь​

Answer 1

ОДЗ : x > 0  ;  y > 0  ;  y > x

$\left \{ {{log_{5}x }+log_{5}y=2+2log_{5}4\atop {log_{81}(y-x)=0,5}} \right.\\\\\left \{ {{log_{5} xy}=log_{5}25+log_{5}16\atop {log_{81}(y-x)=0,5 }} \right.\\\\\left \{ {{log_{5}xy=log_{5}400} \atop {log_{81}(y-x)=0,5 }} \right.$

$\left \{ {{xy=400} \atop {y-x=9}} \right.\\\\\left \{ {{y=x+9} \atop {x(x+9)=400}} \right. \\\\\left \{ {{y=x+9} \atop {x^{2}+9x-400=0 }} \right.\\\\x^{2}+9x-400=0\\\\x_{1}=16\\\\x_{2}=-25<0\\\\y=x+9=16+9=25\\\\Otvet:(16;25)$