EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Logarithms
Grade : ICSE Grade IX
License : Non Commercial Use
Question
1
1.
If
log
2
x
=
a
and
log
2
y
=
b
, then
2
(
a
−
b
)
=
(i)
a
y
(ii)
y
x
(iii)
a
b
(iv)
x
y
(v)
x
b
Question
2
2.
log
40
96
+
log
18
52
=
(i)
log
17
104
(ii)
log
15
104
(iii)
log
1
8
(iv)
log
2
(
15
104
)
(v)
log
5
34
Question
3
3.
If
(
x
2
+
y
2
)
=
214
x
y
, then
2
log
(
x
+
y
)
=
(i)
log
x
−
log
y
+
3
log
6
(ii)
log
x
+
log
y
+
3
log
6
(iii)
log
x
−
log
y
−
3
log
6
(iv)
log
x
+
log
y
−
3
log
6
Question
4
4.
log
2.0000
+
log
8.0000
=
(i)
log
16.0000
(ii)
log
14.0000
(iii)
log
15.0000
(iv)
log
17.0000
(v)
log
18.0000
Question
5
5.
If
log
2 = 0.3010,
log
3 = 0.4771,
log
5 = 0.6989,
log
7 = 0.8451,
the characteristic of
log
105
3
=
(i)
6
(ii)
5
(iii)
4
(iv)
7
(v)
8
Question
6
6.
If
(
x
3
+
y
3
)
=
z
3
, then which of the following is true?
(i)
log
x
(
z
−
y
)
−
log
x
(
z
2
+
z
y
+
y
2
)
=
3
(ii)
log
x
(
z
−
y
)
+
log
x
(
z
2
+
z
y
+
y
2
)
=
6
(iii)
log
x
(
z
−
y
)
+
log
x
(
z
2
+
z
y
+
y
2
)
=
3
(iv)
log
(
z
−
y
)
log
(
z
2
+
z
y
+
y
2
)
=
4
(v)
log
x
(
z
−
y
)
+
log
x
(
z
2
+
z
y
+
y
2
)
=
5
Question
7
7.
Solve
log
x
log
9
=
log
36
log
1
6
(i)
(
-1
81
)
(ii)
1
81
(iii)
1
27
(iv)
1
83
(v)
1
79
Question
8
8.
log
40
57
−
log
17
80
=
(i)
log
1066
323
(ii)
log
2
(
3200
969
)
(iii)
log
3200
967
(iv)
log
3200
969
(v)
log
3202
969
Question
9
9.
log
100.4200
−
log
65.5700
=
(i)
log
2.5315
(ii)
log
9.5315
(iii)
log
3.5315
(iv)
log
0.5315
(v)
log
1.5315
Question
10
10.
log
38.6200
+
log
33.2100
=
(i)
log
1282.5702
(ii)
log
1284.5702
(iii)
log
1280.5702
(iv)
log
1281.5702
(v)
log
1283.5702
Question
11
11.
log
0.1571
−
log
0.6429
=
(i)
log
7.2444
(ii)
log
8.2444
(iii)
log
1.2444
(iv)
log
0.2444
(v)
log
2.2444
Question
12
12.
log
3
7
69
=
(i)
log
7
69
−
log
3
(ii)
log
7
69
✕
log
3
(iii)
log
3
÷
log
7
69
(iv)
log
7
69
÷
log
3
(v)
log
7
69
+
log
3
Question
13
13.
If
(
x
4
+
y
4
)
=
34
x
2
y
2
, then
log
(
x
2
+
y
2
)
=
(i)
log
x
+
log
y
−
log
6
(ii)
log
x
−
log
y
−
log
6
(iii)
log
x
−
log
y
+
log
6
(iv)
log
x
+
log
y
+
log
6
Question
14
14.
Express
log
10
√
p
3
q
r
5
s
in terms of
log
10
p
,
log
10
q
,
log
10
r
and
log
10
s
(i)
3
2
log
10
p
−
1
2
log
10
q
+
5
log
10
r
−
log
10
s
(ii)
3
2
log
10
p
+
1
2
log
10
q
+
5
log
10
r
−
log
10
s
(iii)
3
2
log
10
p
−
1
2
log
10
q
−
5
log
10
r
+
log
10
s
(iv)
3
2
log
10
p
+
1
2
log
10
q
−
5
log
10
r
−
log
10
s
(v)
3
2
log
10
p
−
1
2
log
10
q
−
5
log
10
r
−
log
10
s
Question
15
15.
Find the value of
x
if
log
x
1
9
=
-2
(i)
3
(ii)
2
(iii)
4
(iv)
5
(v)
0
Question
16
16.
Express
log
3
√
p
3
q
2
in terms of
log
p
and
log
q
(i)
3
log
p
+
2
log
q
(ii)
2
log
q
−
3
log
p
(iii)
3
log
p
−
2
log
q
(iv)
3
2
log
p
log
q
(v)
log
p
+
2
3
log
q
Question
17
17.
log
1
2
3
4
=
(i)
log
3
4
✕
log
1
2
(ii)
log
3
4
−
log
1
2
(iii)
log
1
2
÷
log
3
4
(iv)
log
3
4
÷
log
1
2
(v)
log
3
4
+
log
1
2
Question
18
18.
log
8
+
log
3
=
(i)
log
23
(ii)
log
26
(iii)
log
24
2
(iv)
log
24
(v)
log
22
Question
19
19.
log
4
43
+
log
11
53
=
(i)
log
4
207
(ii)
log
42
2279
(iii)
log
2
(
44
2279
)
(iv)
log
46
2279
(v)
log
44
2279
Question
20
20.
log
9
91
5
=
(i)
log
7
89
5
(ii)
6
log
9
91
(iii)
4
log
9
91
(iv)
5
log
9
91
(v)
5
log
9
94
Question
21
21.
log
0.5526
+
log
0.5652
=
(i)
log
1.3124
(ii)
log
7.3124
(iii)
log
8.3124
(iv)
log
0.3124
(v)
log
2.3124
Question
22
22.
log
60.0000
−
log
1.0000
=
(i)
log
60.0000
(ii)
log
61.0000
(iii)
log
58.0000
(iv)
log
62.0000
(v)
log
59.0000
Question
23
23.
log
36
1296
=
(i)
3
(ii)
0
(iii)
1
(iv)
2
(v)
4
Question
24
24.
log
8
16
=
(i)
1.3333
(ii)
3.3333
(iii)
0.3333
(iv)
9.3333
(v)
2.3333
Question
25
25.
Express
log
10
x
y
4
z
5
in terms of
log
10
x
,
log
10
y
and
log
10
z
(i)
log
10
x
+
4
log
10
y
−
5
log
10
z
(ii)
log
10
x
−
4
log
10
y
+
5
log
10
z
(iii)
log
10
x
−
5
log
10
z
+
4
log
10
y
(iv)
log
10
x
−
4
log
10
y
−
5
log
10
z
(v)
log
10
x
+
4
log
10
y
+
5
log
10
z
Assignment Key
1) (iv)
2) (ii)
3) (ii)
4) (i)
5) (i)
6) (iii)
7) (ii)
8) (iv)
9) (v)
10) (i)
11) (iv)
12) (iv)
13) (iv)
14) (iv)
15) (i)
16) (v)
17) (iv)
18) (iv)
19) (v)
20) (iv)
21) (iv)
22) (i)
23) (iv)
24) (i)
25) (i)
