Question

| log3 (x) | > (1/2)        (по основанию 3)

Answer 1

$|log_{3}x|>frac{1}{2}$                              ОДЗ: x>0

 

$log_{3}x>frac{1}{2}$               и              $log_{3}x<-frac{1}{2}$

 

$x>3^frac{1}{2}$                                       $x<3^{-frac{1}{2}}$

 

$x>sqrt{3}$                                               $x<frac{1}{sqrt{3}}$

   

                                                                            $x<frac{sqrt{3}}{3}$

 

Учитывая ОДЗ получим ответ:  $xin(0;frac{sqrt{3}}{3})cup(sqrt{3};+infty)$