EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Logarithms
Grade : ICSE Grade IX
License : Non Commercial Use
Question
1
1.
log
40.0000
+
log
73.0000
=
(i)
log
2919.0000
(ii)
log
2922.0000
(iii)
log
2920.0000
(iv)
log
2921.0000
(v)
log
2918.0000
Question
2
2.
log
91
10
2
3
=
(i)
3
log
91
10
2
(ii)
3
log
91
10
5
(iii)
2
log
91
10
2
(iv)
log
89
10
(-1)
3
(v)
4
log
91
10
2
Question
3
3.
log
49
2401
=
(i)
3
(ii)
2
(iii)
0
(iv)
1
(v)
4
Question
4
4.
log
92
−
log
93
=
(i)
log
92
93
(ii)
log
94
93
(iii)
log
2
(
92
93
)
(iv)
log
92
91
(v)
log
30
31
Question
5
5.
log
1
6
+
log
5
52
=
(i)
log
7
312
(ii)
log
1
104
(iii)
log
2
(
5
312
)
(iv)
log
1
62
(v)
log
5
312
Question
6
6.
If
x
=
1
+
log
c
a
b
;
y
=
1
+
log
a
b
c
;
z
=
1
+
log
b
a
c
,
then which of the following is true?
(i)
(
x
+
y
+
z
)
=
x
y
z
(ii)
(
x
y
−
x
z
−
y
z
)
=
x
y
z
(iii)
(
x
y
+
x
z
−
y
z
)
=
x
y
z
(iv)
(
x
y
+
x
z
+
y
z
)
=
x
y
z
(v)
(
x
y
−
x
z
+
y
z
)
=
x
y
z
Question
7
7.
log
17
28
−
log
47
89
=
(i)
log
1513
1314
(ii)
log
1515
1316
(iii)
log
2
(
1513
1316
)
(iv)
log
1513
1316
(v)
log
1511
1316
Question
8
8.
log
43.0000
−
log
92.0000
=
(i)
log
7.4674
(ii)
log
2.4674
(iii)
log
0.4674
(iv)
log
1.4674
(v)
log
8.4674
Question
9
9.
If
x
=
y
2
(
y
−
1
)
, then
log
(
x
−
y
)
=
(i)
log
x
−
log
y
(ii)
log
x
log
y
(iii)
log
x
log
y
(iv)
log
x
+
log
y
Question
10
10.
Express
log
p
2
q
in terms of
log
p
and
log
q
(i)
2
log
p
log
q
(ii)
log
q
−
2
log
p
(iii)
2
log
p
+
log
q
(iv)
2
log
p
−
log
q
Question
11
11.
log
45
84
+
log
9
53
=
(i)
log
2
(
135
1484
)
(ii)
log
19
212
(iii)
log
137
1484
(iv)
log
45
494
(v)
log
135
1484
Question
12
12.
If
(
x
4
+
y
4
)
=
23
x
2
y
2
, then
log
(
x
2
+
y
2
)
=
(i)
log
x
−
log
y
−
log
5
(ii)
log
x
+
log
y
−
log
5
(iii)
log
x
−
log
y
+
log
5
(iv)
log
x
+
log
y
+
log
5
Question
13
13.
If
log
8
y
+
2
log
8
x
=
2
express
y
in terms of
x
(i)
y
=
64
x
2
(ii)
y
=
64
x
(iii)
y
=
x
64
(iv)
y
=
x
2
64
Question
14
14.
Solve
log
x
log
4
=
log
36
log
1
6
(i)
1
14
(ii)
(
-1
16
)
(iii)
3
16
(iv)
1
18
(v)
1
16
Question
15
15.
The base of
log
1
2
2
15
is
(i)
3
2
(ii)
2
15
(iii)
(
-1
2
)
(iv)
1
2
(v)
1
Question
16
16.
log
9
81
=
(i)
0
(ii)
1
(iii)
3
(iv)
2
(v)
4
Question
17
17.
Find the value of
x
if
log
x
1
4
=
-2
(i)
1
(ii)
(-1)
(iii)
2
(iv)
4
(v)
3
Question
18
18.
If
log
3
x
=
p
and
log
3
y
=
q
, then
x
y
=
(i)
3
p
q
(ii)
3
2
p
q
(iii)
3
(
p
+
q
)
(iv)
3
(
p
−
q
)
Question
19
19.
log
46
3
−
log
46
2
=
(i)
log
48
(ii)
log
46
(iii)
log
46
2
(iv)
log
45
(v)
log
44
Question
20
20.
If
(
x
4
+
y
4
)
=
z
4
, then which of the following is true?
(i)
log
(
z
2
−
y
2
)
log
(
z
2
+
y
2
)
=
5
(ii)
log
x
(
z
2
−
y
2
)
+
log
x
(
z
2
+
y
2
)
=
4
(iii)
log
x
(
z
2
−
y
2
)
−
log
x
(
z
2
+
y
2
)
=
4
(iv)
log
x
(
z
2
−
y
2
)
+
log
x
(
z
2
+
y
2
)
=
7
(v)
log
x
(
z
2
−
y
2
)
+
log
x
(
z
2
+
y
2
)
=
6
Question
21
21.
log
10
900
=
(i)
2
log
2
+
2
log
6
+
2
log
5
(ii)
2
log
2
+
2
log
3
+
2
log
5
(iii)
2
log
2
+
2
log
3
+
3
log
5
(iv)
log
2
+
2
log
3
+
2
log
5
(v)
2
log
2
+
2
log
1
+
2
log
5
Question
22
22.
log
5
8
9
16
=
(i)
log
9
16
−
log
5
8
(ii)
log
5
8
÷
log
9
16
(iii)
log
9
16
÷
log
5
8
(iv)
log
9
16
+
log
5
8
(v)
log
9
16
✕
log
5
8
Question
23
23.
If
log
2 = 0.3010,
log
3 = 0.4771,
log
5 = 0.6989,
log
7 = 0.8451,
the value of
log
135
40
108
40
is
(i)
0.9545
(ii)
1.9545
(iii)
2.9545
(iv)
8.9545
(v)
7.9545
Question
24
24.
The base of
log
10
43
80
is
(i)
9
(ii)
13
(iii)
8
(iv)
43
80
(v)
10
Question
25
25.
log
4
5
73
8
=
(i)
8
5
log
4
73
(ii)
8
5
log
4
75
(iii)
16
5
log
4
73
(iv)
8
5
log
4
72
(v)
8
5
log
1
70
Assignment Key
1) (iii)
2) (i)
3) (ii)
4) (i)
5) (v)
6) (iv)
7) (iv)
8) (iii)
9) (i)
10) (iii)
11) (v)
12) (iv)
13) (i)
14) (v)
15) (iv)
16) (iv)
17) (iii)
18) (iii)
19) (ii)
20) (ii)
21) (ii)
22) (iii)
23) (i)
24) (v)
25) (i)
