EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Logarithms
Grade : ICSE Grade IX
License : Non Commercial Use
Question
1
1.
log
10
540
=
(i)
2
log
2
+
3
log
1
+
log
5
(ii)
2
log
4
+
3
log
3
+
log
5
(iii)
2
log
2
+
3
log
3
+
log
4
(iv)
3
log
2
+
3
log
3
+
log
5
(v)
2
log
2
+
3
log
3
+
log
5
Question
2
2.
log
2
7
+
log
2
4
=
(i)
log
2
10
(ii)
log
2
11
(iii)
log
5
11
(iv)
log
2
12
(v)
log
2
8
Question
3
3.
If
log
2 = 0.3010,
log
3 = 0.4771,
log
5 = 0.6989,
log
7 = 0.8451,
the value of
log
294
14
108
28
is
(i)
0.6475
(ii)
9.6475
(iii)
3.6475
(iv)
2.6475
(v)
1.6475
Question
4
4.
If
log
4
x
=
a
and
log
4
y
=
b
, then
4
(
a
+
1
)
=
(i)
4
y
(ii)
4
a
(iii)
4
b
(iv)
4
(v)
4
x
Question
5
5.
log
9
81
=
(i)
3
(ii)
2
(iii)
1
(iv)
0
(v)
4
Question
6
6.
log
28
−
log
70
=
(i)
log
4
5
(ii)
log
2
3
(iii)
log
-2
(
2
5
)
(iv)
log
2
5
(v)
log
2
(
2
5
)
Question
7
7.
The base of
log
8
9
9
25
is
(i)
10
9
(ii)
2
3
(iii)
9
25
(iv)
8
7
(v)
8
9
Question
8
8.
log
10
5
54
=
(i)
log
5
−
log
2
−
3
log
5
(ii)
log
4
−
log
2
−
3
log
3
(iii)
log
5
−
log
-1
−
3
log
3
(iv)
log
5
−
log
2
−
3
log
3
(v)
2
log
5
−
log
2
−
3
log
3
Question
9
9.
log
181
20
50
6
=
(i)
6
log
181
20
50
(ii)
6
log
181
20
52
(iii)
5
log
181
20
50
(iv)
7
log
181
20
50
(v)
log
179
20
48
6
Question
10
10.
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
11
11.
Find the value of
x
if
log
√
3
(
−
5
x
+
6
)
=
2
(i)
3
7
(ii)
1
(iii)
1
5
(iv)
3
5
Question
12
12.
log
10
22
=
(i)
log
22
−
log
10
(ii)
log
10
÷
log
22
(iii)
log
22
✕
log
10
(iv)
log
22
÷
log
10
(v)
log
22
+
log
10
Question
13
13.
If
(
x
2
+
y
2
)
=
11
x
y
, then
log
(
x
−
y
)
=
(i)
1
2
log
x
−
1
2
log
y
−
log
3
(ii)
1
2
log
x
+
1
2
log
y
−
log
3
(iii)
1
2
log
x
−
1
2
log
y
+
log
3
(iv)
1
2
log
x
+
1
2
log
y
+
log
3
Question
14
14.
If
(
x
2
+
y
2
)
=
z
2
, then which of the following is true?
(i)
log
x
(
z
+
y
)
+
log
x
(
z
−
y
)
=
4
(ii)
log
x
(
z
+
y
)
+
log
x
(
z
−
y
)
=
2
(iii)
log
(
z
+
y
)
log
(
z
−
y
)
=
3
(iv)
log
x
(
z
+
y
)
+
log
x
(
z
−
y
)
=
5
(v)
log
x
(
z
+
y
)
−
log
x
(
z
−
y
)
=
2
Question
15
15.
The base of
log
8
6
7
is
(i)
6
7
(ii)
6
(iii)
8
(iv)
10
(v)
7
Question
16
16.
The base of
log
9
83
is
(i)
12
(ii)
7
(iii)
9
(iv)
83
(v)
8
Question
17
17.
log
52.0000
+
log
46.0000
=
(i)
log
2394.0000
(ii)
log
2391.0000
(iii)
log
2390.0000
(iv)
log
2392.0000
(v)
log
2393.0000
Question
18
18.
log
2
7
=
(i)
log
2
63
✕
log
7
63
(ii)
log
2
63
+
log
7
63
(iii)
log
2
63
÷
log
7
63
(iv)
log
2
63
−
log
7
63
(v)
log
7
63
÷
log
2
63
Question
19
19.
The base exponent form of
log
6
7776
=
5
is
(i)
6
6
=
7776
(ii)
9
5
=
7776
(iii)
6
5
=
7776
(iv)
5
6
=
7776
(v)
6
4
=
7776
Question
20
20.
log
100
7
+
log
100
8
=
(i)
log
102
15
(ii)
log
100
16
(iii)
log
98
15
(iv)
log
100
14
(v)
log
100
15
Question
21
21.
log
15
+
log
60
=
(i)
log
898
(ii)
log
900
(iii)
log
903
(iv)
log
900
2
(v)
log
899
Question
22
22.
log
7
4
60
7
=
(i)
7
4
log
7
59
(ii)
7
4
log
7
63
(iii)
7
2
log
7
60
(iv)
7
4
log
4
58
(v)
7
4
log
7
60
Question
23
23.
log
71
85
+
log
1
2
=
(i)
log
69
170
(ii)
log
2
(
71
170
)
(iii)
log
73
170
(iv)
log
71
170
(v)
log
71
168
Question
24
24.
Find the value of
x
if
log
8
(
x
+
4
)
−
log
8
(
x
−
4
)
=
1
(i)
38
7
(ii)
46
9
(iii)
26
5
(iv)
34
7
(v)
36
7
Question
25
25.
If
(
x
2
+
y
2
)
=
341
x
y
, then
2
log
(
x
+
y
)
=
(i)
log
x
+
log
y
−
3
log
7
(ii)
log
x
−
log
y
−
3
log
7
(iii)
log
x
−
log
y
+
3
log
7
(iv)
log
x
+
log
y
+
3
log
7
Assignment Key
1) (v)
2) (ii)
3) (v)
4) (v)
5) (ii)
6) (iv)
7) (v)
8) (iv)
9) (i)
10) (iii)
11) (iv)
12) (iv)
13) (iv)
14) (ii)
15) (iii)
16) (iii)
17) (iv)
18) (iii)
19) (iii)
20) (v)
21) (ii)
22) (v)
23) (iv)
24) (v)
25) (iv)
