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Byju's Answer
Standard XI
Mathematics
Logarithmic Inequalities
Let a,b∈ℝ+ su...
Question
Let
a
,
b
∈
R
+
such that
log
27
a
+
log
9
b
=
7
2
and
log
27
b
+
log
9
a
=
2
3
.
Then the value of
a
b
is
A
2
7
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B
7
2
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C
3
5
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D
5
3
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Solution
The correct option is
C
3
5
log
27
a
+
log
9
b
=
7
2
⇒
1
3
log
3
a
+
1
2
log
3
b
=
7
2
⇒
2
log
3
a
+
3
log
3
b
=
21
⋯
(
1
)
log
27
b
+
log
9
a
=
2
3
⇒
1
2
log
3
a
+
1
3
log
3
b
=
2
3
⇒
3
log
3
a
+
2
log
3
b
=
4
⋯
(
2
)
Adding equations
(
1
)
and
(
2
)
, we get
5
log
3
a
+
5
log
3
b
=
25
⇒
5
log
3
(
a
b
)
=
25
⇒
log
3
(
a
b
)
=
5
∴
a
b
=
3
5
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0
Similar questions
Q.
Let
a
,
b
∈
R
+
such that
log
27
a
+
log
9
b
=
7
2
and
log
27
b
+
log
9
a
=
2
3
.
Then the value of
a
b
is
Q.
Suppose that
a
and
b
are positive real numbers, such that
log
27
a
+
log
9
b
=
7
2
and
log
27
b
+
log
9
a
=
2
3
, then find the value of
a
b
Q.
Suppose that
a
and
b
are two positive real numbers such that
log
27
a
+
log
9
b
=
7
2
and
log
27
b
+
log
9
a
=
2
3
, then the value of product
a
b
is
Q.
Let A =
(
p
q
r
s
]
and B =
(
a
b
]
≠
(
0
0
]
. Such that AB = B and p+s = 2, then find the value of (ps-qr).