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Byju's Answer
Standard XIII
Mathematics
Logarithmic Inequalities
The solution ...
Question
The solution set of
log
2
|
4
−
5
x
|
>
2
is
A
(
8
5
,
∞
)
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B
(
4
5
,
8
5
)
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C
(
−
∞
,
0
)
∪
(
8
5
,
∞
)
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D
none of these
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Solution
The correct option is
C
(
−
∞
,
0
)
∪
(
8
5
,
∞
)
We have
log
2
|
4
−
5
x
|
>
2
|
4
−
5
x
|
>
0
⇒
x
∈
R
−
{
4
5
}
Now
log
2
|
4
−
5
x
|
>
2
⇒
|
4
−
5
x
|
>
2
2
(
if base is greater than 1 then inequality remains same
)
⇒
|
4
−
5
x
|
>
4
⇒
4
−
5
x
<
−
4
or
4
−
5
x
>
4
⇒
x
>
8
5
or
x
<
0
∴
x
∈
(
−
∞
,
0
)
∪
(
8
5
,
∞
)
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Standard XIII Mathematics
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