Question

Неравенство с логарифмами!
Заранее спасибо!

Answer 1

X>0
log(2)x=t
(t-5)/(1-2t)-2t≥0
(t-5-2t+4t²)/(t-1)≤0
(4t²-t-5)/(2t-1)≤0
4t²-t-5=0
D=1+80=81
t1=(1-9)/8=-1
t2=(1+9)/8=5/4
2t-1=0
t=0,5
  _                   +           _                  +
-------[-1]----------(0,5)----------[1,25]-----
t≤-1⇒log(2)x≤-1⇒x≤0,5
0,5<t≤5/4⇒0,5<log(2)x≤5/4⇒$\sqrt{2} \ \textless \ x \leq 2 \sqrt[4]{2}$
x∈(0;0,5] U ($( \sqrt{2} ;2 \sqrt[4]{2]}$