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Byju's Answer
Standard XII
Mathematics
Average Rate of Change
If a2+b2=7 ...
Question
If
a
2
+
b
2
=
7
a
b
, then prove that
log
(
a
+
b
3
)
=
1
2
(
log
a
+
log
b
)
Open in App
Solution
a
2
+
b
2
=
7
a
b
⇒
(
a
+
b
)
2
−
2
a
b
=
7
a
b
⇒
(
a
+
b
)
2
=
9
a
b
⇒
(
a
+
b
3
)
2
=
a
b
Taking log on both sides, we get
⇒
log
(
a
+
b
3
)
2
=
log
a
b
⇒
2
log
(
a
+
b
3
)
=
log
a
+
log
b
(
∵
log
x
m
=
m
log
x
;
log
m
n
=
log
m
+
log
n
)
⇒
log
(
a
+
b
3
)
=
1
2
(
log
a
+
log
b
)
Suggest Corrections
2
Similar questions
Q.
If
a
2
+
b
2
=
7
a
b
, prove that
2
log
(
a
+
b
)
=
log
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+
log
a
+
log
b
Q.
If
a
2
+
b
2
=
7
a
b
. Prove that
log
(
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(
a
+
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)
)
=
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[
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]
Q.
If
a
2
−
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a
b
+
4
b
2
=
0
, prove that
log
(
a
+
2
b
)
=
1
2
(
log
a
+
log
b
)
+
2
log
2
Q.
If
a
2
+
b
2
=
23
a
b
, show that:
log
a
+
b
5
=
1
2
(
log
a
+
log
b
)
.
Q.
If
a
2
+
b
2
=
3
a
b
,
show that
log
(
a
+
b
√
5
)
=
1
2
(
log
a
+
log
b
)
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