Question

Помогите решить log0,5(1-3x) больше или равно -2

Answer 1

$log_{0.5}(1-3x) geq -2\ ===================\ 1-3x textgreater 0\ -3x textgreater -1\ x textless frac{1}{3} \ ===================\ log_{0.5}(1-3x) geq -2cdot log_{0.5}0.5\ log_{0.5}(1-3x) geq log_{0.5}( frac{1}{2} )^{-2}\ log_{0.5}(1-3x) geq log_{0.5}4\ 0 textless 0.5 textless 1 Rightarrow \ 1-3x leq 4\ -3x leq 3\ x geq -1\ ===================\\ left { {{x textless frac{1}{3}} atop {x geq -1}} right. Rightarrow x in [-1; frac{1}{3} )$