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Byju's Answer
Standard XII
Mathematics
Fundamental Laws of Logarithms
log2 , log(2^...
Question
\log2 , \log (2^n-1 ) , \log( 2^n+3) are in ap then n=
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Q.
If
a
1
,
a
2
,
a
3
,
.
.
.
are in GP then the values of the determinant
∣
∣ ∣
∣
l
o
g
a
1
log
a
n
+
1
log
a
2
n
+
1
l
o
g
a
2
log
a
n
+
2
log
a
2
n
+
2
l
o
g
a
3
log
a
n
+
3
log
a
2
n
+
3
∣
∣ ∣
∣
is
Q.
If
log
2
,
log
(
2
x
−
1
)
and
log
(
2
x
+
3
)
are in AP , then the value of
x
is given by
Q.
If in an AP,
t
1
=
log
10
a
,
t
n
+
1
=
log
10
b
and
t
2
n
+
1
=
log
10
c
then
a
,
b
,
c
are in
Q.
f
(
x
)
=
lim
n
→
∞
log
(
2
+
x
)
−
x
2
n
sin
x
1
+
x
2
n
.Then
Q.
Assertion :When
|
x
|
<
1
,
lim
n
→
∞
log
(
x
+
2
)
−
x
2
n
c
o
s
x
x
2
n
+
1
=
log
(
x
+
2
)
. Reason: For
−
1
<
x
<
1
, as
n
→
∞
,
x
2
n
→
0
.
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