[tex]\displaystyle\bf\\y=\log_{x-2} (10-x)\\\\\\\left\{\begin{array}{ccc}x-2 > 0\\x\neq 1\\10-x > 0\end{array}\right \\\\\\\left\{\begin{array}{ccc}x > 2\\x\neq 1\\-x > -10\end{array}\right \\\\\\\left\{\begin{array}{ccc}x > 2\\x\neq 1\\x < 10\end{array}\right \\\\\\Otvet \ : \ D(y)=(2 \ ; \ 10)[/tex]