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Byju's Answer
Standard X
Mathematics
Solving Inequalities
Let S = log...
Question
Let S =
log
2
(
√
7
+
√
5
)
, then find the value of
log
2
(
√
7
−
√
5
)
in terms of S :
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Solution
S
=
log
2
(
√
7
+
√
5
)
log
2
(
√
7
+
√
5
)
+
log
2
(
√
7
−
√
5
)
=
log
2
(
7
−
5
)
=
1
S
+
log
2
(
√
7
−
√
5
)
=
1
⟹
log
2
(
√
7
−
√
5
)
=
1
−
S
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0
Similar questions
Q.
Solve the equation
log
2
(
3
−
x
)
−
log
2
(
s
i
n
3
π
4
5
−
x
)
=
1
2
+
log
2
(
x
+
7
)
Q.
If
log
2
(
3
2
x
−
2
+
7
)
=
2
+
log
2
(
3
x
−
1
+
1
)
, then value of
x
is equal to
Q.
The value of
log
2
7
is:
Q.
Show that
log
6
7
=
l
o
g
2
7
1
+
l
o
g
2
3
Q.
If
log
2
=
a
a
n
d
log
3
=
b
then
[
log
(
1
)
+
log
(
1
+
3
)
+
log
(
1
+
3
+
5
)
+
.
.
.
+
.
.
.
+
log
(
1
+
3
+
5
+
7
+
.
.
.
+
19
)
]
-
2
[
log
1
+
log
2
+
log
3
+
.
.
.
+
log
7
]
=
p
+
q
a
+
r
b
where
p
,
q
,
r
are constants. What is the value of
p
+
2
q
+
3
r
if all logs are in base
10
?
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