EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Logarithms
Grade : ICSE Grade IX
License : Non Commercial Use
Question
1
1.
log
9
27
=
(i)
0.5
(ii)
1.5
(iii)
3.5
(iv)
2.5
(v)
9.5
Question
2
2.
If
log
3
x
=
a
and
log
3
y
=
b
, then
3
(
a
−
b
)
=
(i)
x
y
(ii)
x
b
(iii)
a
b
(iv)
y
x
(v)
a
y
Question
3
3.
If
(
x
4
+
y
4
)
=
7
x
2
y
2
, then
log
(
x
2
+
y
2
)
=
(i)
log
x
−
log
y
−
log
3
(ii)
log
x
+
log
y
−
log
3
(iii)
log
x
−
log
y
+
log
3
(iv)
log
x
+
log
y
+
log
3
Question
4
4.
log
19
50
−
log
2
5
=
(i)
log
19
18
(ii)
log
19
20
(iii)
log
2
(
19
20
)
(iv)
log
21
20
(v)
log
17
20
Question
5
5.
If
log
2 = 0.3010,
log
3 = 0.4771,
log
5 = 0.6989,
log
7 = 0.8451,
the mantissa of
log
567
10
=
(i)
0.535
(ii)
8.535
(iii)
2.535
(iv)
1.535
(v)
7.535
Question
6
6.
The base of
log
1
2
63
is
(i)
(
-1
2
)
(ii)
1
2
(iii)
1
(iv)
3
2
(v)
63
Question
7
7.
log
10
4
9
=
(i)
-1
log
2
3
(ii)
3
log
2
3
(iii)
log
2
3
(iv)
2
log
2
3
(v)
2
log
4
3
Question
8
8.
log
81
729
=
(i)
9.5
(ii)
1.5
(iii)
3.5
(iv)
2.5
(v)
0.5
Question
9
9.
Solve
log
x
log
8
=
log
49
log
1
7
(i)
1
66
(ii)
(
-1
64
)
(iii)
3
64
(iv)
1
62
(v)
1
64
Question
10
10.
log
52.0000
+
log
43.0000
=
(i)
log
2238.0000
(ii)
log
2236.0000
(iii)
log
2235.0000
(iv)
log
2234.0000
(v)
log
2237.0000
Question
11
11.
If
(
x
2
+
y
2
)
=
14
x
y
, then
2
log
(
x
+
y
)
=
(i)
log
x
+
log
y
−
2
log
4
(ii)
log
x
−
log
y
+
2
log
4
(iii)
log
x
−
log
y
−
2
log
4
(iv)
log
x
+
log
y
+
2
log
4
Question
12
12.
Find the value of
x
if
log
x
625
=
4
(i)
5
(ii)
3
(iii)
8
(iv)
6
(v)
4
Question
13
13.
The base of
log
9
7
is
(i)
8
(ii)
11
(iii)
9
(iv)
7
Question
14
14.
log
10
972
=
(i)
log
2
+
5
log
3
(ii)
2
log
2
+
5
log
3
(iii)
3
log
2
+
5
log
3
(iv)
2
log
4
+
5
log
3
(v)
2
log
2
+
5
log
1
Question
15
15.
If
(
x
2
+
y
2
)
=
51
x
y
, then
log
(
x
−
y
)
=
(i)
1
2
log
x
+
1
2
log
y
+
log
7
(ii)
1
2
log
x
−
1
2
log
y
+
log
7
(iii)
1
2
log
x
+
1
2
log
y
−
log
7
(iv)
1
2
log
x
−
1
2
log
y
−
log
7
Question
16
16.
log
17
7
+
log
17
2
=
(i)
log
17
9
(ii)
log
17
8
(iii)
log
17
10
(iv)
log
14
9
(v)
log
19
9
Question
17
17.
log
25
125
=
(i)
1.5
(ii)
2.5
(iii)
0.5
(iv)
9.5
(v)
3.5
Question
18
18.
If
log
(
x
2
+
16
)
log
2
x
2
=
1
, find x
(i)
(
-2
,
4
)
(ii)
(
-4
,
3
)
(iii)
(
-3
,
5
)
(iv)
(
3
,
-4
)
(v)
(
-4
,
4
)
Question
19
19.
log
100
1000
=
(i)
3.5
(ii)
1.5
(iii)
0.5
(iv)
2.5
(v)
9.5
Question
20
20.
log
32
10
+
log
32
6
=
(i)
log
32
17
(ii)
log
29
16
(iii)
log
32
16
(iv)
log
32
15
(v)
log
34
16
Question
21
21.
Find the value of
x
if
log
x
1
16
=
-4
(i)
2
(ii)
1
(iii)
3
(iv)
(-1)
(v)
4
Question
22
22.
If
log
8
x
=
p
and
log
8
y
=
q
, then
x
y
=
(i)
8
p
q
(ii)
8
(
p
−
q
)
(iii)
8
2
p
q
(iv)
8
(
p
+
q
)
Question
23
23.
log
10
2
43
8
=
(i)
7
log
10
2
43
(ii)
log
8
2
41
8
(iii)
9
log
10
2
43
(iv)
8
log
10
2
43
(v)
8
log
10
2
45
Question
24
24.
Find the value of
x
if
log
(
x
+
2
)
+
log
(
x
−
2
)
=
log
7
(i)
(
√
11
,
(
−
11
)
)
(ii)
(
11
,
(
−
11
)
)
(iii)
(
11
,
(
−
√
11
)
)
(iv)
(
√
11
,
(
−
√
11
)
)
Question
25
25.
The base exponent form of
log
3
243
=
5
is
(i)
3
5
=
243
(ii)
6
5
=
243
(iii)
3
6
=
243
(iv)
5
3
=
243
(v)
3
4
=
243
Assignment Key
1) (ii)
2) (i)
3) (iv)
4) (ii)
5) (i)
6) (ii)
7) (iv)
8) (ii)
9) (v)
10) (ii)
11) (iv)
12) (i)
13) (iii)
14) (ii)
15) (i)
16) (i)
17) (i)
18) (v)
19) (ii)
20) (iii)
21) (i)
22) (iv)
23) (iv)
24) (iv)
25) (i)
