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Byju's Answer
Standard XII
Mathematics
Logarithmic Inequalities
Find the solu...
Question
Find the solution set of the given inequality:
3
log
3
√
x
−
1
<
3
log
3
(
x
−
6
)
+
3
A
(
5
,
+
∞
)
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B
(
6
,
+
∞
)
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C
(
1
,
2
)
∪
(
3
,
5
)
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D
(
−
∞
,
2
)
∪
(
5
,
∞
)
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Solution
The correct option is
C
(
6
,
+
∞
)
3
log
3
√
x
−
1
<
3
log
3
(
x
−
6
)
+
3
⇒
√
x
−
1
log
3
3
<
(
x
−
6
)
log
3
3
+
3
⇒
√
x
−
1
<
(
x
−
6
)
+
3
⇒
√
x
−
1
<
x
−
3
Squaring both sides,
(
x
−
1
)
<
(
x
−
3
)
2
⇒
x
−
1
<
x
2
−
6
x
+
9
⇒
x
2
−
7
x
+
10
>
0
⇒
(
x
−
5
)
(
x
−
2
)
>
0
⇒
x
ϵ
(
−
∞
,
2
)
∪
(
5
,
∞
)
But,
x
−
6
>
0
⇒
x
>
6
∴
x
ϵ
(
6
,
∞
)
Suggest Corrections
0
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