The number of integers satisfying the inequality 
< 
(4 – log 16 x 4 ) are
Text Solution
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Domain x > 0
log 22 x + 2 log 2 x ≥ 0
log 2 x (log 2 x + 2) ≥ 0
log 2 x ≤ – 2 or log 2 x ≥ 0
0 < x ≤ 
or x ≥ 1
x ∈ 
∪ [1, ∞ ) .......(i)
Case-I 4 – log 2 x < 0
positive <negative (false)
Case-II 4 – log 2 x ≥ 0 ⇒ log 2 x ≤ 4
⇒ log 22 x 2 log 2 x < 2 (4 – log 2 x) 2
Let log 2 x = t
t 2 + 2t < 2 (4 – t) 2
t 2 – 18t + 32 > 0
(t – 16) (t – 2) > 0
⇒ t < 2 ∪ t > 16
log 2 x < 2 ∪ log 2 x > 16 (Rejected )
log 2 x < 2
x < 4 .........(ii)
by (i) and (ii)
x ∈ 
∪ [1, 4)
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