Question

Найти область определения функции.

Answer 1

$f(x)=\sqrt{log_{5}(x-2)-log_{5}7}\\\\\left \{ {{log_{5}(x-2)-log_{5}7\geq0} \atop {x-2>0}} \right. \\\\\left \{ {{log_{5}(x-2)\geq log_{5}7} \atop {x>2}} \right.\\\\\left \{ {{x-2\geq7 } \atop {x>2}} \right.\\\\\left \{ {{x\geq 9} \atop {x>2}} \right.\Rightarrow x\geq9\\\\Otvet:\boxed{x\in[9; \ +\infty)}$