Question

Добрий вечір, будь ласка

Answer 1

 ОДЗ  :

$\displaystyle\bf\\\left \{ {{x\neq 1} \atop {x > 0}} \right. \\\\\\1+2\log_{x}5=\log_{5} x \\\\\\1+\frac{2}{\log_{5}x } -\log_{5} x=0\\\\\\\frac{\log^{2} _{5}x-\log_{5}x -2 }{\log_{5} x} =0\\\\\\\log_{5}x=m \ \ , \ \ m\neq 0\\\\m^{2} -m-2=0\\\\(m-2)\cdot(m+1)=0\\\\\\\left[\begin{array}{ccc}m-2=0\\m+1=0\end{array}\right \ \ \Rightarrow \ \ \left[\begin{array}{ccc}m_{1} =2\\m_{2} =-1\end{array}\right$

$\displaystyle\bf\\1)\\\\\log_{5} x=2\\\\x_{1} =5^{2} =25\\\\2)\\\\\log_{5} x=-1\\\\x_{2} =5^{-1} =\frac{1}{5} =0,2\\\\Otvet \ : \ 25 \ \ ; \ \ 0,2$