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Logarithms
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Quiz-1 : Numbers, General Mathematics
Quiz-2 : HCF & LCM, General Mathematics
Quiz-3 : Decimal Fractions, General Mathematics
Quiz-7 : Percentage, General Mathematics
Quiz-8 : Profit and Loss, General Mathematics
Quiz-10 : Partnership, General Mathematics
Quiz-11 : Time & Work, General Mathematics
Index
General Mathematics Home
HCF & LCM
49
Numbers
118
Decimal Fractions
80
Roots
1
Percentage
114
Profit and Loss
32
Compound Interest
44
Average
54
Surds and Indices
35
Ratio & Proportion
107
Time & Work
47
Partnership
20
Simplification
94
Simple Interest
61
Area & Volume
113
Logarithms
41
Discount
17
Problems On Boats & Streams
14
Area
98
Chain Rule
17
odd man out and series
47
Alligation or Mixture
23
Latest Questions
139
Rances & Games of Skill
59
Schools
Ebook
Question:
If
log
10
2
=
0.30103
, the value of
log
10
50
is :
A
.69897
B
1.30103
C
1.69897
D
2.30103
Note:
log
10
50
=
log
10
(
100
2
)
=
log
10
100
-
log
10
2
=
2
-
0.30103
=
1.69897
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Question:
If
log
10
2
=
0.3010
, the value of
log
10
80
is :
A
1.9030
B
1.6020
C
3.9030
D
None of these
Note:
log
10
80
=
log
10
(
8
×
10
)
=
log
10
8
+
log
10
10
=
log
10
2
3
+
1
=
(
3
log
10
2
)
+
1
=
(
3
×
0.3010
)
+
1
=
1.9030
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Question:
If
log
10
2
=
0.3010
,
the value of
log
10
25
is :
A
1.5050
B
1.3980
C
1.2040
D
0.6020
Note:
log
10
25
=
log
10
(
100
4
)
=
log
10
100
-
log
10
4
=
2
-
2
log
10
2
=
(
2
-
2
×
0.3010
)
=
(
2
-
0.6020
)
=
1.3980
.
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Question:
The value of
(
log
9
27
+
log
8
32
)
is :
A
4
B
7
C
7
2
D
19/6
Note:
≤
t
log_9 27 = x.
T
h
e
n
,
9^x = 27 ⇔ (3^2)^x
= 3^3
:. 3^2x = 3^3.
So, 2x = 3
or x = 3/2.
≤
t
log_8 32 = y.
T
h
e
n
,
8^y = 32
or (2^3)^y = 2^5.
:.2^3y = 2^5.
S
o
,
3y = 5
or y = 5/3
.
:. log_9 27 + log_8 32
= (3/2 + 5/3)
= 19/6.
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Question:
I
f
log_4 x + log_2 x = 6,
t
h
e
n
t
h
e
v
a
l
u
e
o
f
x
i
s
:
A
2
B
4
C
8
D
16
Note:
Given equation is
log
x
log
4
+
log
x
log
2
=
6
or
log
x
2
log
2
+
log
x
log
2
=
6
or
3
log
x
=
12
log
2
.
∴
log
x
=
4
log
2
=
log
2
4
.
S
o
,
x
=
16
.
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Question:
If
log
10
(
0.1
)
=
-
1
,
then
log
10
(
.001
)
is :
A
-
1.3
B
-
2
C
-
2.3
D
-
3
Note:
log
10
(
.001
)
=
log
10
(
.1
100
)
=
log
10
(
.1
)
-
log
10
(
100
)
=
(
-
1
-
2
)
=
-
3
.
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Question:
If
log
5
(
x
2
+
x
)
-
log
5
(
x
+
1
)
=
2
,
then the value of x is :
A
5
B
32
C
25
D
10
Note:
log
5
(
x
2
+
x
)
-
log
5
(
x
+
1
)
=
2
⇒
log
5
(
x
2
+
x
x
+
1
)
=
2
∴
log
5
[
(
x
x
+
1
x
+
1
]
=
2
or
log
5
x
=
2
or
x
=
5
2
=
25
.
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Question:
If
log
5
(
x
2
+
x
)
-
log
5
(
x
+
1
)
=
2
,
then the value of x is :
A
5
B
32
C
25
D
10
Note:
log
5
(
x
2
+
x
)
-
log
5
(
x
+
1
)
=
2
⇒
log
5
(
x
2
+
x
x
+
1
)
=
2
∴
log
5
[
(
x
x
+
1
x
+
1
]
=
2
or
log
5
x
=
2
or
x
=
5
2
=
25
.
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Question:
If log x + log y = log (x + y), then :
A
x
=
y
B
x
y
=
1
C
y
=
x
-
1
x
D
y
=
x
x
-
1
Note:
log
x
+
log
y
=
log
(
x
+
y
)
⇒
log
(
x
+
y
)
=
log
(
x
y
)
∴
x
+
y
=
x
y
or
y
(
x
-
1
)
=
x
or
y
=
x
x
-
1
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Question:
If
log
10
125
+
log
10
8
=
x
,
then x is equal to :
A
3
B
-
3
C
1
3
D
.064
Note:
log
10
125
+
log
10
8
=
x
⇒
log
10
(
125
×
8
)
=
x
.
∴
x
=
log
10
(
1000
)
=
log
10
(
10
3
)
=
3
log
10
10
=
(
3
×
1
)
=
3
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