Решите неравенство. (Log 0,5 x)^2 - 3log 0,5 x - 4 <= 0

Question

Решите неравенство. (Log 0,5 x)^2 - 3log 0,5 x - 4 <= 0<hr>

Answer 1

(Log (0.5, x))^2 - 3log( 0.5, x )- 4 <= 0<br>D=9+16=25
1) log(0.5,x)=(3+5)/2=4
2) log(0.5,x)=(3-5)/2=-1

(log(0.5,x)-4)(log(0.5,x)+1)<=0<br>(x-(0.5)^4)(x-(0.5)^(-1))<=0<br>(x-0.0625)(x-2)<=0<br>
ОТВЕТ : x∈[0.0625;2]

Answer 2

(log(0,5)x)²-3log(0,50x-4≤0
ОДЗ
x>0
x∈(0;∞)
log(0,5)x=t
t²-3t-4≤0
t1+t2=3 U t1*t2=-4
t1=-1 U 2=4
  +                _                  +
--------[-1]------------[4]--------------
-1≤t≤4
-1≤log(0,5)≤4
0,0625≤x≤2
x∈[0,0625;2]