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The solution ...
Question
The solution set of the inequality
log
0.5
√
x
−
4
x
−
3
<
log
0.5
2
is
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Solution
Given,
log
0.5
√
x
−
4
x
−
3
<
log
0.5
2
log
function is defined when
√
x
−
4
x
−
3
>
0
⇒
x
∈
(
−
∞
,
3
)
∪
(
4
,
∞
)
Now,
1
2
log
0.5
(
x
−
4
x
−
3
)
<
log
0.5
2
⇒
log
0.5
(
x
−
4
x
−
3
)
<
log
0.5
4
⇒
x
−
4
x
−
3
>
4
⇒
x
−
4
−
4
x
+
12
x
−
3
>
0
⇒
3
x
−
8
x
−
3
<
0
⇒
x
∈
(
8
3
,
3
)
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