Question
If log0.04(x−1)≥log0.2(x−1) then x belongs to the interval
Answer: Option C
:
C
log0.04(x−1)≥log0.2(x−1) ....(i)
For log to be defined x−1>0⇒x>1
From(i),log(0.2)2(x−1)≥log0.2(x−1)
⇒12log0.2(x−1)≥log0.2(x−1)⇒√x−1≤(x−1)⇒√x−1(1−√x−1)≤0⇒1−√x−1≤0⇒√x−1≥1⇒x≥2,∴xϵ[2,∞).
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:
C
log0.04(x−1)≥log0.2(x−1) ....(i)
For log to be defined x−1>0⇒x>1
From(i),log(0.2)2(x−1)≥log0.2(x−1)
⇒12log0.2(x−1)≥log0.2(x−1)⇒√x−1≤(x−1)⇒√x−1(1−√x−1)≤0⇒1−√x−1≤0⇒√x−1≥1⇒x≥2,∴xϵ[2,∞).
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