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The number of integers satisfying $\log_{\frac{1}{x}} (\frac{2 (x - 2)}{(x + 1) (x - 5)}) \geq 1 is$

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Correct option is A

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

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The number of integers satisfying $\log_{\frac{1}{x}} (\frac{2 (x - 2)}{(x + 1) (x - 5)}) \geq 1 is$