Question:
If log0.04(x – 1) ≥ log0.2(x – 1) , then x belongs to the interval.
If log0.04(x – 1) ≥ log0.2(x – 1) , then x belongs to the interval.
Options:
- [2, ∞)
- [2, -1)
- (1, 2]
- (-∞, 2]
- [2, ∞)
- [2, -1)
- (1, 2]
- (-∞, 2]
Correct Answer: a)
Explanation:
‘ We ha√e, log 4 (z — 1) > log ,(z — 1) …(1)
‘ For log to be defined x-1>0=x>1 ‘
‘ From Eq. (i), log; (= —1) >logg,(z —1) ‘
= 3logg,(z — 1) > logy ,(z — 1)
=√aI<@-1) '
= √a I(1-√a 1)<0 !
=1-√z—-1<0
‘ Vz I>1=z>2
‘ Lx € (2,00)
‘ We ha√e, log 4 (z — 1) > log ,(z — 1) …(1)
‘ For log to be defined x-1>0=x>1 ‘
‘ From Eq. (i), log; (= —1) >logg,(z —1) ‘
= 3logg,(z — 1) > logy ,(z — 1)
=√aI<@-1) '
= √a I(1-√a 1)<0 !
=1-√z—-1<0
‘ Vz I>1=z>2
‘ Lx € (2,00)