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Q.

The number of integers satisfying log1x⁡2(x−2)(x+1)(x−5)≥1 is

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a

0

b

1

c

2

d

3

answer is A.

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Detailed Solution

Case I: 1/x>1 or 00  since x2+5 >0 for all x∈R⇒ x∈(−1,0)∪(5,∞)Hence, no solution in this case. Case II: 0<1x<1 or x>1   →1 ∴ 00  ⇒x∈ -1,2∪5,∞→ 3  from 1,2,3 we can take  x∈(1,2)
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The number of integers satisfying log1x⁡2(x−2)(x+1)(x−5)≥1 is