Решите подробно! 20 баллов.

$x^{0,5\log_5{x}}= \frac{5}{ \sqrt{x}}\\\\ x^{\log_5{ \sqrt{x}}}=\frac{5}{ \sqrt{x}}\\\\ \log_x{\frac{5}{ \sqrt{x}}=\log_5 \sqrt{x}}= \frac{1}{2}\log_5{x}= \frac{1}{2}\cdot \frac{1}{\log_x{5}} \\\\ \log_x5-\log_x{ \sqrt{x}}=\frac{1}{2}\cdot \frac{1}{\log_x{5}}\\\\ \log_x{5}- \frac{1}{2}=\frac{1}{2}\cdot \frac{1}{\log_x{5}}\\\\ \log_x{5}=t\\\\ t- \frac{1}{2}= \frac{1}{2t}\\\\ \frac{2t-1}{2}= \frac{1}{2t}\\\\ 4t^2-2t=2\\\\ 4t^2-2t-2=0\\\\ 2t^2-t-1=0\\\\ D=1+8=9; \ \sqrt{D}=3$

$t_{1/2}= \frac{1\pm3}{4}\\\\ t_1=1; \ t_2=-\frac{1}{2}\\\\ \log_x{5}=1\\ x^{1}=5\\\\ \log_x{5}=-\frac {1}{2}\\ \frac{1}{\sqrt{x}}=5\\ x=\frac{1}{25}$

Ответ: $x_1= \frac{1}{25} ; x_2={5}$