Byju's Answer
Standard XII
Mathematics
Logarithmic Inequalities
If 2 log 3 x ...
Question
If
2
log
3
x
−
4
log
x
27
≤
5
(
x
>
1
)
, then the number of integral values of
x
is
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Solution
2
log
3
x
−
4
log
x
27
≤
5
⇒
2
log
3
x
−
4
⋅
3
log
x
3
≤
5
Let
log
3
x
=
y
⇒
2
y
−
12
y
≤
5
⇒
2
y
2
−
5
y
−
12
≤
0
[
As
x
>
1
⇒
y
>
0
]
⇒
(
2
y
+
3
)
(
y
−
4
)
≤
0
⇒
y
∈
[
−
3
2
,
4
]
But
y
>
0
∴
0
<
y
≤
4
⇒
0
<
log
3
x
≤
4
⇒
1
<
x
≤
81
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