find the number of positive integers not satisfying the inequality log of (t^2 -2t+17) to base 2 is greater than 5
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㏒₂(t²-2t+17) >5
(t-1)²+16>32
(t-1)²>16
case (i)
t-1>4
t>5..............................t∈(5, ∞)
case (ii)
t-1<-4
t<-3.............................t∈(-∞,-3)
so t∈(-∞,-3)∪(5, ∞)
so here satisfying is t∈(5, ∞)
(t-1)²+16>32
(t-1)²>16
case (i)
t-1>4
t>5..............................t∈(5, ∞)
case (ii)
t-1<-4
t<-3.............................t∈(-∞,-3)
so t∈(-∞,-3)∪(5, ∞)
so here satisfying is t∈(5, ∞)
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