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Byju's Answer
Standard XI
Mathematics
Logarithmic Inequalities
The domain of...
Question
The domain of definition of
f
(
x
)
=
√
log
(
log
x
)
−
log
(
4
−
log
x
)
−
log
3
is
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Solution
Given,
f
(
x
)
=
√
log
(
log
x
)
−
log
(
4
−
log
x
)
−
log
3
Thus
log
(
log
x
)
−
log
(
4
−
log
x
)
−
log
2
⩾
0
⇒
log
(
(
log
x
)
(
4
−
log
x
)
3
)
⩾
0
⇒
log
x
(
4
−
log
x
)
3
⩾
1
Put
log
x
=
t
Therefore,
4
t
−
t
2
−
2
⩾
0
⇒
t
2
−
4
t
+
3
≤
0
⇒
t
ϵ
[
1
,
3
]
⇒
log
x
ϵ
[
1
,
3
]
Thus
x
ϵ
[
10
3
,
10
4
]
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