Question

log5 (x^2 -3x -4) + 2/(log3(0,2) <0

Answer 1

$log_5 (x^2-3x-4)+frac{2}{log_3 0.2} textless 0 \ x^2-3x-4 textgreater 0; (x-4)(x+1) textgreater 0; left { {{x textgreater 4} atop {x textless -1}} right. \ xin (-infty;-1) cup (4;+infty) \\ log_5 (x^2-3x-4)+frac{2}{log_3 frac{1}{5} } textless 0 \ log_5 (x^2-3x-4)-frac{2}{log_3 5 } textless 0 \ log_5 (x^2-3x-4)-2log_5 3 textless 0 \ log_5 frac{x^2-3x-4}{9} textless log_5 1 \ frac{x^2-3x-4}{9} textless 1 \ x^2-3x-13 textless 0 \ D=(-3)^2-4*(-13)=9+52=61 \ x=frac{3pmsqrt{61}}{2} \ (x-frac{3+sqrt{61}}{2})(x-frac{3-sqrt{61}}{2}) textless 0$
$\ frac{3-sqrt{61}}{2} textless x textless frac{3+sqrt{61}}{2} \\ xin (frac{3-sqrt{61}}{2};-1)cup(4;frac{3+sqrt{61}}{2})$