Question

Решить неравенство
log0,9 (x - 4) ≥ log0,9 (8 - x)

Answer 1

ОДЗ :

$\left \{ {{x-4>0} \atop {8-x>0}} \right.\\\\\left \{ {{x>4} \atop {x<8}} \right. \ \Rightarrow \ x\in(4 \ ; \ 8)\\\\\\log_{0,9} (x-4)\geq log_{0,9}(8-x)\\\\0<0,9<1 \ \Rightarrow \ x-4\leq 8-x\\\\x+x\leq8+4\\\\2x\leq12\\\\x\leq 6\\\\Otvet:\boxed{x\in(4 \ ; \ 6]}$