Question

$frac{log_{2}(10-x) }{log_{1/2}(x+11) } textless 0$

Answer 1

ОДЗ 10-x>0⇒x<10 U x+11>0⇒x>-11
x∈(-11;10)
1){log(2)(10-x)<0⇒10-x<1⇒x>9
   {log(1/2)(x+11)>0⇒x+11<1⇒x<-10
решения нет
2){log(2)(10-x)>0⇒10-x>1⇒x<9
   {log(1/2)(x+11)<0⇒x+11>1⇒x>-10
Ответ x∈(-10;9)