Question

$lg(2x+24) leq lg( x^{2} -3x)$

Answer 1

$lg(2x+24) leq lg(x^2-3x) \ 2x+24 leq x^2-3x \ -x^2+5x+24 leq 0 \ x^2-5x-24 geq 0 \ left { {{x geq 8} atop {x leq -3}} right.$
ОДЗ:
$left { {{2x+24 textgreater 0} atop {x^2-3x textgreater 0}} right. \ left { {{2x textgreater -24} atop {x(x-3) textgreater 0}} right. \ left { {{x textgreater -12} atop {x textless 0; x textgreater 3}} right.$

Ответ: (-12;-3] U [8;+∞)