[tex]5^x=\frac{1}{25}\\\\5^x=25^{-1}\\\\5^x=(5^2)^{-1}\\\\5^x=5^{-2}\\\\\underline{x=-2}[/tex]

[tex]x^2-8x+7=0\\\\x^2-x-7x+7\\\\x(x-1)-7(x-1)=0\\\\(x-1)(x-7)=0\\\\x-1=0\ \ \ \ \ \ \ \ \ \ x-7=0\\\\\underline{x=1}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \underline{x=7}[/tex]

[tex]2x^2-5x+2=0\\\\2x^2-4x-x+2=0\\\\2x(x-2)-(x-2)=0\\\\(x-2)(2x-1)=0\\\\x-2=0\ \ \ \ \ \ \ \ \ \ 2x-1=0\\\\\underline{x=2}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 2x=1\ \ \ |:2\\\\.\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \underline{x=\frac{1}{2}}[/tex]