Question

помогите пожалуйста log 1/2(3-2x)>-1

Answer 1

$log_{ frac{1}{2} }(3-2x) textgreater -1$
ОДЗ:
$3-2x textgreater 0$
$-2x textgreater -3$
$x textless 1.5$
$log_{ frac{1}{2} }(3-2x) textgreater log_{ frac{1}{2} }( frac{1}{2})^{-1}$
$3-2x textless ( frac{1}{2})^{-1}$
$3-2x textless 2$
$-2x textless 2-3$
$-2x textless -1$
$x textgreater 0.5$
              ///////////////////////////////////////
------(0.5)--------------(1.5)----------------
 ////////////////////////////////
 
 Ответ: (0.5; 1.5)