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AIEEE 2002 Math Solved Paper
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Section:
Mathematics
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© examsnet.com
Question : 22
Total: 74
If
1
,
log
9
(
3
1
−
x
+
2
)
,
log
3
(
4.3
x
−
1
)
are in A.P. then
x
equals
[AIEEE 2002]
log
3
4
1
−
log
3
4
1
−
log
4
3
log
4
3
Validate
Solution:
1
,
log
9
(
3
1
−
x
+
2
)
,
log
3
(
4.3
x
−
1
)
are in
A
.
P
.
⇒
2
log
9
(
3
1
−
x
+
2
)
=
1
+
log
3
(
4.3
x
−
1
)
⇒
log
3
(
3
1
−
x
+
2
)
=
log
3
3
+
log
3
(
4.3
x
−
1
)
⇒
log
3
(
3
1
−
x
+
2
)
=
log
3
[
3
(
4.3
x
−
1
)
]
⇒
3
1
−
x
+
2
=
3
(
4.3
x
−
1
)
⇒
3.3
−
x
+
2
=
12.3
x
−
3
Put
3
x
=
t
⇒
‌
3
t
+
2
=
12
t
−
3
or
12
t
2
−
5
t
−
3
=
0
Hence
t
=
−
‌
1
3
,
‌
3
4
⇒
3
x
=
‌
3
4
(as
3
x
â‰
−
v
e
)
⇒
x
=
log
3
(
‌
3
4
)
or
x
=
log
3
3
−
log
3
4
⇒
x
=
1
−
log
3
4
© examsnet.com
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