Question

Помогите с системой пожалуйста

Answer 1

$\left \{ {{2log_{0,5}\, x+log_{0,5}\, y=-4} \atop {lgx-lgy=lg0,5}} \right. \; \; ,\; \; ODZ:\; \; x\ \textgreater \ 0,\; y\ \textgreater \ 0\\\\a)\; \; 2log_{0,5}\, x+log_{0,5}\, y=-4\; \; \to \; \; log_{0,5}\, x^2+log_{0,5}\, y=log_{0,5}(0,5)^{-4}\\\\x^2\cdot y=( \frac{1}{2})^{-4}\; ,\; \; x^2\cdot y=2^4\; ,\; \; \underline {x^2\cdot y=16}\\\\b)\; \; lgx-lgy=lg \frac{1}{2}\; ,\; \; lg \frac{x}{y}=lg \frac{1}{2}\; ,\; \; \frac{x}{y}=\frac{1}{2}\; ,\; \; \underline {2x=y}\\\\c)\; \; x^2\cdot y=x^2\cdot 2x=2x^3\\\\2x^3=16\; ,\; \; x^3=8\; ,\; \; \underline {x=2}\\\\y=2x=2\cdot 2\; ,\; \; \underline {y=4}\\\\Otvet:\; \; (2,4)\; .$