If log0.04(x−1)≥log0.2(x−1), then x belongs to the interval
A
(1,2]
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B
(−∞,2]
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C
[2,∞)
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D
none of these
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Solution
The correct option is C[2,∞) log0.04(x−1)≥log0.2(x−1) ⇒log(0.2)2(x−1)≥log0.2(x−1) ⇒12log0.2(x−1)≥log0.2(x−1) ⇒log0.2(x−1)≥2log0.2(x−1) ⇒log0.2(x−1)≤0⇒(x−1)≥(0.2)0⇒x≥2⇒x∈[2,∞)