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Byju's Answer
Standard XII
Mathematics
Logarithmic Inequalities
The solution ...
Question
The solution set of the inequality
(
log
10
x
)
4
−
13
(
log
10
x
)
2
+
36
>
0
is
A
(
1000
,
∞
)
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B
(
1
100
,
100
)
∪
(
1000
,
∞
)
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C
(
0
,
100
)
∪
(
1000
,
∞
)
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D
(
0
,
1
1000
)
∪
(
1
100
,
100
)
∪
(
1000
,
∞
)
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Solution
The correct option is
D
(
0
,
1
1000
)
∪
(
1
100
,
100
)
∪
(
1000
,
∞
)
Given,
(
log
10
x
)
4
−
13
(
log
10
x
)
2
+
36
>
0
,
x
>
0
⇒
[
(
log
10
x
)
2
−
4
]
[
(
log
10
x
)
2
−
9
]
>
0
⇒
(
log
10
x
+
2
)
(
log
10
x
−
2
)
(
log
10
x
+
3
)
(
log
10
x
−
3
)
>
0
⇒
log
10
x
∈
(
−
∞
,
−
3
)
∪
(
−
2
,
2
)
∪
(
3
,
∞
)
⇒
x
∈
(
0
,
1
1000
)
∪
(
1
100
,
100
)
∪
(
1000
,
∞
)
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Standard XII Mathematics
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