Question

Помогите пожалуйста log3(8x^2+x)> 2+log3 x^2+log3 x

Answer 1

$log_3(8x^2+x) textgreater 2 + log_3(x^2) + log_3(x)\ log_3(8x^2+x) textgreater log_3(9) + log_3(x^2) + log_3(x)\ log_3(8x^2+x) textgreater log_3(9x^3) \ 8x^2+x textgreater 9x^3\ 9x^3-8x^2-x textless 0\ x(9x^2-8x-1) textless 0\ x in (-infty; -frac{1}{9}) cup (0;1)\\ 8x^2+x textgreater 0\ x(8x+1) textgreater 0\ x in (-infty; -frac{1}{8}) cup (0; +infty)\\ x textgreater 0\ x in (0; +infty)\\ x in ((-infty; -frac{1}{9}) cup (0;1)) cap ((-infty; -frac{1}{8}) cup (0; +infty)) cap (0; +infty)\ x in (0;1)$