Question

Пожалуйста, нужна помощь с логарифмами
Решите систему уравнений
$left { {{log _{2}x-log_4y=0 } atop {log_4x+log_2y=1}} right.$

Answer 1

$left { {{log_{2}x-log_{2^{2}}y=0} atop {log_{2^{2}}x+log_{2}y=1}} right.$

$left { {{log_{2}x-0.5*log_{2}y=0} atop {0.5*log_{2}x+log_{2}y=1}} right.$

$left { {{log_{2}x-log_{2}(sqrt{y})=0} atop {log_{2}(sqrt{x})+log_{2}y=1}} right.$

$left { {{log_{2}(frac{x}{sqrt{y}})=log_{2}1} atop {log_{2}(sqrt{x}*y)=log_{2}2}} right.$

$left { {{frac{x}{sqrt{y}}=1} atop {sqrt{x}*y=2} right.$

$left { {{x=sqrt{y}} atop {sqrt{x}*y=2} right.$

$left { {{x^{2}=y} atop {sqrt{x}*x^{2}=2} right.$

$left { {{x^{2}=y} atop {x^{frac{5}{2}}=2} right.$

$left { {{x^{2}=y} atop {x=2^{frac{2}{5}}} right.$

$left { {{y=(2^{frac{2}{5}})^{2}=2^{frac{4}{5}}} atop {x=2^{frac{2}{5}}} right.$

Ответ: (2²/⁵; 2⁴/⁵)