EduSahara™ Assignment
Name : Logarithmic Expressions involving Variables
Chapter : Logarithms
Grade : ICSE Grade IX
License : Non Commercial Use
Question
1
1.
Express
log
10
x
2
y
2
z
3
in terms of
log
10
x
,
log
10
y
and
log
10
z
(i)
2
log
10
x
−
2
log
10
y
−
3
log
10
z
(ii)
2
log
10
x
−
2
log
10
y
+
3
log
10
z
(iii)
2
log
10
x
−
3
log
10
z
+
2
log
10
y
(iv)
2
log
10
x
+
2
log
10
y
+
3
log
10
z
(v)
2
log
10
x
+
2
log
10
y
−
3
log
10
z
Question
2
2.
If
log
5
y
+
2
log
5
x
=
2
express
y
in terms of
x
(i)
y
=
x
2
25
(ii)
y
=
x
25
(iii)
y
=
25
x
2
(iv)
y
=
25
x
Question
3
3.
Express
log
10
a
2
c
4
√
b
in terms of
log
10
a
,
log
10
b
and
log
10
c
(i)
2
log
10
a
+
4
log
10
c
−
1
2
log
10
b
(ii)
4
log
10
c
−
1
2
log
10
b
+
2
log
10
a
(iii)
2
log
10
a
+
4
log
10
c
+
1
2
log
10
b
(iv)
2
log
10
a
−
4
log
10
c
+
1
2
log
10
b
(v)
2
log
10
a
−
4
log
10
c
−
1
2
log
10
b
Question
4
4.
Express
log
5
√
p
3
q
3
r
4
s
3
in terms of
log
5
p
,
log
5
q
,
log
5
r
and
log
5
s
(i)
3
2
log
5
p
−
3
2
log
5
q
+
4
log
5
r
−
3
log
5
s
(ii)
3
2
log
5
p
+
3
2
log
5
q
+
4
log
5
r
−
3
log
5
s
(iii)
3
2
log
5
p
−
3
2
log
5
q
−
4
log
5
r
+
3
log
5
s
(iv)
3
2
log
5
p
−
3
2
log
5
q
−
4
log
5
r
−
3
log
5
s
(v)
3
2
log
5
p
+
3
2
log
5
q
−
4
log
5
r
−
3
log
5
s
Question
5
5.
If
log
8
x
=
p
and
log
8
y
=
q
, then
x
y
=
(i)
8
2
p
q
(ii)
8
p
q
(iii)
8
(
p
+
q
)
(iv)
8
(
p
−
q
)
Question
6
6.
If
log
4
x
=
p
and
log
4
y
=
q
, then
x
y
=
(i)
4
p
q
(ii)
4
2
p
q
(iii)
4
(
p
−
q
)
(iv)
4
(
p
+
q
)
Question
7
7.
Express
log
10
x
4
y
z
in terms of
log
10
x
,
log
10
y
and
log
10
z
(i)
4
log
10
x
−
log
10
y
+
log
10
z
(ii)
4
log
10
x
−
log
10
z
+
log
10
y
(iii)
4
log
10
x
+
log
10
y
+
log
10
z
(iv)
4
log
10
x
+
log
10
y
−
log
10
z
(v)
4
log
10
x
−
log
10
y
−
log
10
z
Question
8
8.
If
log
4
y
+
4
log
4
x
=
2
express
y
in terms of
x
(i)
y
=
x
4
16
(ii)
y
=
16
x
4
(iii)
y
=
x
16
(iv)
y
=
16
x
Question
9
9.
Express
log
9
a
3
c
√
b
in terms of
log
9
a
,
log
9
b
and
log
9
c
(i)
3
log
9
a
+
log
9
c
−
1
2
log
9
b
(ii)
3
log
9
a
−
log
9
c
+
1
2
log
9
b
(iii)
3
log
9
a
−
log
9
c
−
1
2
log
9
b
(iv)
log
9
c
−
1
2
log
9
b
+
3
log
9
a
(v)
3
log
9
a
+
log
9
c
+
1
2
log
9
b
Question
10
10.
Express
log
10
√
p
3
q
4
r
2
s
5
in terms of
log
10
p
,
log
10
q
,
log
10
r
and
log
10
s
(i)
3
2
log
10
p
−
2
log
10
q
+
2
log
10
r
−
5
log
10
s
(ii)
3
2
log
10
p
−
2
log
10
q
−
2
log
10
r
+
5
log
10
s
(iii)
3
2
log
10
p
+
4
2
log
10
q
+
2
log
10
r
−
5
log
10
s
(iv)
3
2
log
10
p
−
2
log
10
q
−
2
log
10
r
−
5
log
10
s
(v)
3
2
log
10
p
+
4
2
log
10
q
−
2
log
10
r
−
5
log
10
s
Question
11
11.
If
log
5
x
=
p
and
log
5
y
=
q
, then
x
y
=
(i)
5
2
p
q
(ii)
5
(
p
−
q
)
(iii)
5
(
p
+
q
)
(iv)
5
p
q
Question
12
12.
If
log
2
x
=
p
and
log
2
y
=
q
, then
x
y
=
(i)
2
(
p
−
q
)
(ii)
2
p
q
(iii)
2
2
p
q
(iv)
2
(
p
+
q
)
Question
13
13.
If
log
6
x
=
a
and
log
6
y
=
b
, then
6
(
a
+
1
)
=
(i)
6
x
(ii)
6
a
(iii)
6
b
(iv)
6
(v)
6
y
Question
14
14.
If
log
3
x
=
a
and
log
3
y
=
b
, then
3
(
a
+
b
)
=
(i)
3
(ii)
a
b
(iii)
y
b
(iv)
a
x
(v)
x
y
Question
15
15.
If
log
2
x
=
a
and
log
2
y
=
b
, then
2
(
a
−
b
)
=
(i)
x
y
(ii)
x
b
(iii)
a
b
(iv)
a
y
(v)
y
x
Question
16
16.
If
log
8
x
=
a
and
log
8
y
=
b
, then
8
3
b
=
(i)
y
3
(ii)
x
3
(iii)
a
3
(iv)
3
y
(v)
3
b
Question
17
17.
Express
log
p
3
q
2
in terms of
log
p
and
log
q
(i)
3
log
p
+
2
log
q
(ii)
3
log
p
−
2
log
q
(iii)
2
log
q
−
3
log
p
(iv)
3
2
log
p
log
q
Question
18
18.
Express
log
√
p
q
4
in terms of
log
p
and
log
q
(i)
4
log
q
−
log
p
(ii)
log
p
−
4
log
q
(iii)
1
4
log
p
log
q
(iv)
log
p
+
4
log
q
(v)
1
2
log
p
+
2
1
log
q
Question
19
19.
Express
log
3
√
p
2
q
5
in terms of
log
p
and
log
q
(i)
5
log
q
−
2
log
p
(ii)
2
log
p
−
5
log
q
(iii)
2
log
p
+
5
log
q
(iv)
2
3
log
p
+
5
3
log
q
(v)
2
5
log
p
log
q
Question
20
20.
Express
log
p
2
q
in terms of
log
p
and
log
q
(i)
log
q
−
2
log
p
(ii)
2
log
p
−
log
q
(iii)
2
log
p
log
q
(iv)
2
log
p
+
log
q
Question
21
21.
Express
log
√
p
2
q
in terms of
log
p
and
log
q
(i)
log
p
+
1
2
log
q
(ii)
log
p
−
1
2
log
q
(iii)
1
2
log
q
−
log
p
(iv)
2
log
p
log
q
Question
22
22.
If
(
x
2
+
y
2
)
=
47
x
y
, then
2
log
(
x
+
y
)
=
(i)
log
x
−
log
y
−
2
log
7
(ii)
log
x
+
log
y
+
2
log
7
(iii)
log
x
−
log
y
+
2
log
7
(iv)
log
x
+
log
y
−
2
log
7
Question
23
23.
If
(
x
2
+
y
2
)
=
27
x
y
, then
log
(
x
−
y
)
=
(i)
1
2
log
x
−
1
2
log
y
+
log
5
(ii)
1
2
log
x
+
1
2
log
y
−
log
5
(iii)
1
2
log
x
+
1
2
log
y
+
log
5
(iv)
1
2
log
x
−
1
2
log
y
−
log
5
Question
24
24.
If
(
x
4
+
y
4
)
=
47
x
2
y
2
, then
log
(
x
2
+
y
2
)
=
(i)
log
x
+
log
y
+
log
7
(ii)
log
x
+
log
y
−
log
7
(iii)
log
x
−
log
y
+
log
7
(iv)
log
x
−
log
y
−
log
7
Question
25
25.
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
26
26.
If
(
x
2
+
y
2
)
=
z
2
, then which of the following is true?
(i)
log
x
(
z
+
y
)
+
log
x
(
z
−
y
)
=
2
(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
)
=
4
(v)
log
x
(
z
+
y
)
+
log
x
(
z
−
y
)
=
5
Question
27
27.
If
(
x
3
+
y
3
)
=
z
3
, then which of the following is true?
(i)
log
(
z
−
y
)
log
(
z
2
+
z
y
+
y
2
)
=
4
(ii)
log
x
(
z
−
y
)
+
log
x
(
z
2
+
z
y
+
y
2
)
=
5
(iii)
log
x
(
z
−
y
)
+
log
x
(
z
2
+
z
y
+
y
2
)
=
6
(iv)
log
x
(
z
−
y
)
−
log
x
(
z
2
+
z
y
+
y
2
)
=
3
(v)
log
x
(
z
−
y
)
+
log
x
(
z
2
+
z
y
+
y
2
)
=
3
Question
28
28.
If
(
x
4
+
y
4
)
=
z
4
, then which of the following is true?
(i)
log
x
(
z
2
−
y
2
)
−
log
x
(
z
2
+
y
2
)
=
4
(ii)
log
(
z
2
−
y
2
)
log
(
z
2
+
y
2
)
=
5
(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
)
=
6
(v)
log
x
(
z
2
−
y
2
)
+
log
x
(
z
2
+
y
2
)
=
7
Question
29
29.
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
30
30.
If
log
4
x
=
a
and
log
4
y
=
b
, then
4
(
a
+
1
)
=
(i)
4
b
(ii)
4
y
(iii)
4
(iv)
4
a
(v)
4
x
Question
31
31.
If
log
9
x
=
a
and
log
9
y
=
b
, then
9
(
a
+
b
)
=
(i)
a
b
(ii)
a
x
(iii)
y
b
(iv)
9
(v)
x
y
Question
32
32.
If
log
10
x
=
a
and
log
10
y
=
b
, then
10
(
a
−
b
)
=
(i)
y
x
(ii)
a
y
(iii)
x
y
(iv)
x
b
(v)
a
b
Question
33
33.
If
log
6
x
=
a
and
log
6
y
=
b
, then
6
4
b
=
(i)
x
4
(ii)
4
b
(iii)
y
4
(iv)
a
4
(v)
4
y
Question
34
34.
Express
log
p
3
q
in terms of
log
p
and
log
q
(i)
3
log
p
+
log
q
(ii)
log
q
−
3
log
p
(iii)
3
log
p
log
q
(iv)
3
log
p
−
log
q
Question
35
35.
Express
log
√
p
2
q
5
in terms of
log
p
and
log
q
(i)
log
p
+
5
2
log
q
(ii)
2
log
p
−
5
log
q
(iii)
5
log
q
−
2
log
p
(iv)
2
log
p
+
5
log
q
(v)
2
5
log
p
log
q
Question
36
36.
Express
log
3
√
p
2
q
2
in terms of
log
p
and
log
q
(i)
2
log
p
+
2
log
q
(ii)
2
log
q
−
2
log
p
(iii)
log
p
log
q
(iv)
2
3
log
p
+
2
3
log
q
(v)
2
log
p
−
2
log
q
Question
37
37.
Express
log
p
q
2
in terms of
log
p
and
log
q
(i)
2
log
q
−
log
p
(ii)
log
p
−
2
log
q
(iii)
log
p
+
2
log
q
(iv)
1
2
log
p
log
q
Question
38
38.
Express
log
√
p
3
q
3
in terms of
log
p
and
log
q
(i)
3
2
log
q
−
3
2
log
p
(ii)
log
p
log
q
(iii)
3
2
log
p
+
3
2
log
q
(iv)
3
2
log
p
−
3
2
log
q
Question
39
39.
If
(
x
2
+
y
2
)
=
7
x
y
, then
2
log
(
x
+
y
)
=
(i)
log
x
+
log
y
+
2
log
3
(ii)
log
x
+
log
y
−
2
log
3
(iii)
log
x
−
log
y
−
2
log
3
(iv)
log
x
−
log
y
+
2
log
3
Question
40
40.
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
41
41.
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
Assignment Key
1) (v)
2) (iii)
3) (i)
4) (v)
5) (iii)
6) (iii)
7) (iv)
8) (ii)
9) (i)
10) (v)
11) (iii)
12) (i)
13) (i)
14) (v)
15) (i)
16) (i)
17) (i)
18) (v)
19) (iv)
20) (ii)
21) (ii)
22) (ii)
23) (iii)
24) (i)
25) (iv)
26) (i)
27) (v)
28) (iii)
29) (iii)
30) (v)
31) (v)
32) (iii)
33) (iii)
34) (i)
35) (i)
36) (iv)
37) (ii)
38) (iv)
39) (i)
40) (iv)
41) (iii)
