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Byju's Answer
Standard X
Mathematics
Linear Inequations
The range of ...
Question
The range of values of
x
that satisfy the inequation
(
4
x
+
1
−
16
x
<
2
log
4
8
)
is
A
x
∈
(
0
,
log
4
3
)
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B
x
∈
(
0
,
log
3
4
)
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C
x
∈
(
0
,
log
4
3
]
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D
None of these
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Solution
The correct option is
B
x
∈
(
0
,
log
4
3
)
Given,
(
4
x
+
1
−
16
x
<
2
log
4
8
)
Now,
l
o
g
4
8
=
l
o
g
4
2
3
=
3
l
o
g
4
2
=
3
l
o
g
2
4
=
3
2
l
o
g
2
2
=
3
2
.............(1)
Let,
4
x
=
t
then given inequation reduce in the form
4
t
−
t
2
>
2.
3
2
..........from(1)
⇒
t
2
−
4
t
+
3
<
0
⇒
(
t
−
1
)
(
t
−
3
)
<
0
⇒
1
<
t
<
3
⇒
1
<
4
x
<
3
⇒
0
<
x
<
l
o
g
4
3
Hence, the answer is option
A
Suggest Corrections
0
Similar questions
Q.
Solve the following inequality:
log
4
/
3
(
√
x
+
3
−
√
x
)
+
log
4
/
9
(
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3
)
⩾
0
Q.
The range of values of
x
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l
o
g
(
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)
(
2
x
−
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x
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>
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is
Q.
Solve the equation in each of the following.
(i)
log
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)
+
log
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=
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(ii)
log
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)
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(iii)
log
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x
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5
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(vii)
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3
25
+
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3
x
=
3
log
3
5
(viii)
log
3
(
√
5
x
−
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)
−
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=
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(
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+
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)
Q.
Solve:
log
4
log
2
log
√
2
log
3
(
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−
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=
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Q.
Find sum of all integer values of
x
satisfying :
log
2
(
4
−
x
)
+
log
(
4
−
x
)
.
log
(
x
+
1
2
)
−
2
log
2
(
x
+
1
2
)
=
0
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