Question

Помогите пожалуйста Lg(x+12)+lg(x+3)-1<_0

Answer 1

$lg (x+12)+lg(x+3) -1 \leq 0 \\\\ x+12\ \textgreater \ 0;x\ \textgreater \ -12 \\ x+3\ \textgreater \ 0; x\ \textgreater \ -3 \\ x\in (-3; +\infty) \\\\ lg (x+12)(x+3) \leq lg 10 \\ (x+12)(x+3) \leq 10 \\ x^2+15x+36-10 \leq 0 \\ x^2+15x+26 \leq 0 \\ (x+13)(x+2) \leq0 \\ -13\leq x \leq -2 \\\\ x\in (-3;-2]$