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Byju's Answer
Standard XII
Mathematics
Fundamental Laws of Logarithms
If log10 2x+1...
Question
If
log
10
(
2
x
+
1
)
+
2
x
=
log
10
6
+
x
log
10
50
, then the value of
x
is
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Solution
log
10
(
2
x
+
1
)
+
2
x
=
log
10
6
+
x
log
10
50
⇒
log
10
(
2
x
+
1
)
+
2
x
−
x
log
10
(
100
2
)
=
log
10
6
⇒
log
10
(
2
x
+
1
)
+
2
x
−
x
(
log
10
100
−
log
10
2
)
=
log
10
6
⇒
log
10
(
2
x
+
1
)
+
2
x
−
2
x
+
log
10
2
x
=
log
10
6
⇒
log
10
[
(
2
x
+
1
)
2
x
]
=
log
10
6
⇒
2
x
(
2
x
+
1
)
=
6
⇒
(
2
x
)
2
+
2
x
−
6
=
0
⇒
(
2
x
+
3
)
(
2
x
−
2
)
=
0
⇒
2
x
−
2
=
0
as
2
x
+
3
≠
0
⇒
x
=
1
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Q.
If
x
+
log
10
(
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+
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x
)
=
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log
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+
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is
Q.
The number of positive integers satisfying the equation
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10
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x
+
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)
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log
10
5
+
log
10
6
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log
10
x
+
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=
log
10
250
, then
the value of
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10
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is equal to
Q.
If
log
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