EduSahara™ Assignment
Name : Logarithms involving variables
Chapter : Real Numbers
Grade : SSC Grade X
License : Non Commercial Use
Question
1
1.
Express
log
10
x
5
y
4
z
2
in terms of
log
10
x
,
log
10
y
and
log
10
z
(i)
5
log
10
x
−
2
log
10
z
+
4
log
10
y
(ii)
5
log
10
x
+
4
log
10
y
+
2
log
10
z
(iii)
5
log
10
x
−
4
log
10
y
−
2
log
10
z
(iv)
5
log
10
x
+
4
log
10
y
−
2
log
10
z
(v)
5
log
10
x
−
4
log
10
y
+
2
log
10
z
Question
2
2.
If
log
2
y
+
4
log
2
x
=
2
express
y
in terms of
x
(i)
y
=
4
x
4
(ii)
y
=
x
4
4
(iii)
y
=
x
4
(iv)
y
=
4
x
Question
3
3.
Express
log
10
a
3
c
2
√
b
in terms of
log
10
a
,
log
10
b
and
log
10
c
(i)
3
log
10
a
−
2
log
10
c
−
1
2
log
10
b
(ii)
2
log
10
c
−
1
2
log
10
b
+
3
log
10
a
(iii)
3
log
10
a
+
2
log
10
c
+
1
2
log
10
b
(iv)
3
log
10
a
+
2
log
10
c
−
1
2
log
10
b
(v)
3
log
10
a
−
2
log
10
c
+
1
2
log
10
b
Question
4
4.
Express
log
8
√
p
2
q
3
r
2
s
3
in terms of
log
8
p
,
log
8
q
,
log
8
r
and
log
8
s
(i)
log
8
p
−
3
2
log
8
q
+
2
log
8
r
−
3
log
8
s
(ii)
log
8
p
+
3
2
log
8
q
−
2
log
8
r
−
3
log
8
s
(iii)
log
8
p
+
3
2
log
8
q
+
2
log
8
r
−
3
log
8
s
(iv)
log
8
p
−
3
2
log
8
q
−
2
log
8
r
+
3
log
8
s
(v)
log
8
p
−
3
2
log
8
q
−
2
log
8
r
−
3
log
8
s
Question
5
5.
If
log
2
x
=
p
and
log
2
y
=
q
, then
x
y
=
(i)
2
(
p
−
q
)
(ii)
2
p
q
(iii)
2
(
p
+
q
)
(iv)
2
2
p
q
Question
6
6.
If
log
9
x
=
p
and
log
9
y
=
q
, then
x
y
=
(i)
9
2
p
q
(ii)
9
(
p
+
q
)
(iii)
9
p
q
(iv)
9
(
p
−
q
)
Question
7
7.
If
log
4
x
=
a
and
log
4
y
=
b
, then
4
(
a
+
1
)
=
(i)
4
x
(ii)
4
a
(iii)
4
b
(iv)
4
y
(v)
4
Question
8
8.
If
log
3
x
=
a
and
log
3
y
=
b
, then
3
(
a
+
b
)
=
(i)
3
(ii)
a
b
(iii)
a
x
(iv)
y
b
(v)
x
y
Question
9
9.
If
log
8
x
=
a
and
log
8
y
=
b
, then
8
(
a
−
b
)
=
(i)
x
b
(ii)
a
b
(iii)
x
y
(iv)
y
x
(v)
a
y
Question
10
10.
If
log
9
x
=
a
and
log
9
y
=
b
, then
9
2
b
=
(i)
x
2
(ii)
2
y
(iii)
a
2
(iv)
2
b
(v)
y
2
Question
11
11.
Express
log
p
q
5
in terms of
log
p
and
log
q
(i)
log
p
+
5
log
q
(ii)
log
p
−
5
log
q
(iii)
1
5
log
p
log
q
(iv)
5
log
q
−
log
p
Question
12
12.
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
(v)
3
2
log
p
+
1
2
log
q
Question
13
13.
Express
log
3
√
p
q
3
in terms of
log
p
and
log
q
(i)
log
p
+
3
log
q
(ii)
1
3
log
p
log
q
(iii)
3
log
q
−
log
p
(iv)
log
p
−
3
log
q
(v)
1
3
log
p
+
log
q
Question
14
14.
Express
log
p
q
in terms of
log
p
and
log
q
(i)
log
p
log
q
(ii)
log
p
−
log
q
(iii)
log
p
+
log
q
(iv)
log
q
−
log
p
Question
15
15.
Express
log
√
p
q
in terms of
log
p
and
log
q
(i)
1
2
log
p
−
1
2
log
q
(ii)
1
2
log
q
−
1
2
log
p
(iii)
log
p
log
q
(iv)
1
2
log
p
+
1
2
log
q
Question
16
16.
If
(
x
2
+
y
2
)
=
123
x
y
, then
2
log
(
x
+
y
)
=
(i)
log
x
+
log
y
−
3
log
5
(ii)
log
x
−
log
y
+
3
log
5
(iii)
log
x
−
log
y
−
3
log
5
(iv)
log
x
+
log
y
+
3
log
5
Question
17
17.
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
18
18.
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
19
19.
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
20
20.
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
)
=
5
(iii)
log
x
(
z
+
y
)
+
log
x
(
z
−
y
)
=
4
(iv)
log
x
(
z
+
y
)
−
log
x
(
z
−
y
)
=
2
(v)
log
(
z
+
y
)
log
(
z
−
y
)
=
3
Question
21
21.
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
(
z
−
y
)
log
(
z
2
+
z
y
+
y
2
)
=
4
(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
)
=
5
Question
22
22.
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
)
=
7
(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
)
=
4
(v)
log
x
(
z
2
−
y
2
)
+
log
x
(
z
2
+
y
2
)
=
6
Question
23
23.
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
Assignment Key
1) (iv)
2) (i)
3) (iv)
4) (ii)
5) (iii)
6) (iv)
7) (i)
8) (v)
9) (iii)
10) (v)
11) (i)
12) (v)
13) (v)
14) (ii)
15) (i)
16) (iv)
17) (i)
18) (i)
19) (iv)
20) (i)
21) (iv)
22) (iv)
23) (iii)
