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NDA Math Sequences and Series
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© examsnet.com
Question : 75
Total: 79
If
log
10
2
,
log
10
(
2
x
−
1
)
and
log
10
(
2
x
+
3
)
are three consecutive terms of an A.P., then the value of x is
[NDA I 2015]
1
log
s
2
l
o
g
2
5
log
10
5
Validate
Solution:
It is given that the following numbers are in A.P.
log
10
(
2
)
,
log
10
(
2
x
−
1
)
,
log
10
(
2
x
+
3
)
⇒
2
log
10
(
2
x
−
1
)
=
log
10
(
2
)
+
log
10
(
2
x
+
3
)
log
10
(
(
2
x
−
1
)
2
)
=
log
10
(
2
x
+
1
+
6
)
(
2
x
−
1
)
2
=
2
x
+
1
+
6
2
2
x
−
2
x
+
1
+
1
=
2
x
+
1
+
6
2
2
x
−
2
x
+
1
+
5
Let
2
x
=
t
t
2
=
4
t
+
5
t
2
−
4
t
−
5
=
0
(
t
−
5
)
(
t
+
1
)
=
0
t
=
5
,
t
=
−
1
2
x
=
−
1
(not possible)
2
x
=
5
x
=
log
2
(
5
)
© examsnet.com
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