Question

 

Log2(3x+2)-log2(1-2x)>2

Answer 1

ОДЗ
$left { {{3x+2>0} atop {1-2x>0}} right. <=> left { {{3x>-2} atop {-2x>-1}} right. <=>left { {{x>-frac{2}{3}} atop {x<frac{1}{2}}} right. \ (-frac{2}{3};frac{1}{2}})$

$log_2(3x+2)-log_2(1-2x)>2\ log_2frac{3x+2}{1-2x}>2\ frac{3x+2}{1-2x}>2^2\ frac{3x+2}{1-2x}>4\ 3x+2<4(1-2x)\ 3x+2<4-8x\ 3x+8x<4-2\ 11x<2\ x<frac{2}{11}$

учитывая ОДЗ  $(-frac{2}{3};frac{2}{11}})$