[latex]lg(2x+24) \leq lg( x^{2} -3x)[/latex]

[latex]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. [/latex] ОДЗ: [latex] \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.[/latex] Ответ: (-12;-3] U [8;+∞)