#1
(1/2)^(log1/2 (x^2 - 1)) > 1
(1/2)^(log1/2 (x^2 - 1)) > (1/2)^0
log1/2 (x^2 - 1)) < 0
log1/2 (x^2 - 1)) < log 1/2 (1)
x^2 - 1 > 1
x^2 > 2
x^2 - 2 > 0
(x - √2)(x + √2) > 0
ОДЗ
x^2 - 1> 0
(x - 1)(x + 1) > 0
x ∈ (- ∞ ; - 1) ∪ (1; + ∞)
+ - +
--------- (- √2 ) -------------( √2) -----------------> x
Ответ
x ∈ ( - ∞ ; - √2) ∪ (√2; + ∞)
#2
2^(log 2(x^2 + x)) < 2^1
x^2 + x - 2< 0
x ∈ ( - 2; 1)
#3
log81 (x + 2) > 1 /2
36 - x^2 > 0
(6 - x)(6 + x) > 0
log81 (x + 2) > log81 (9)
(x - 6)(x + 6) < 0
x + 2 > 9
x ∈ ( - 6; 6 )
x ∈ (7; + ∞) + одз x > - 2
нет решений ∅