EduSahara™ Assignment
Name : Solving Logarithmic Equations
Chapter : Logarithms
Grade : ICSE Grade IX
License : Non Commercial Use
Question
1
1.
Find the value of
x
if
log
x
125
=
3
(i)
6
(ii)
3
(iii)
5
(iv)
4
(v)
7
Question
2
2.
Find the value of
x
if
log
3
x
=
4
(i)
80
(ii)
79
(iii)
82
(iv)
84
(v)
81
Question
3
3.
Find the value of
x
if
log
4
256
=
x
(i)
6
(ii)
2
(iii)
5
(iv)
4
(v)
3
Question
4
4.
Find the value of
x
if
log
√
4
(
−
6
x
−
5
)
=
2
(i)
(
-5
4
)
(ii)
(
-5
2
)
(iii)
(
-1
2
)
(iv)
-2
(v)
(
-3
2
)
Question
5
5.
Find the value of
x
if
log
x
1
125
=
-3
(i)
6
(ii)
5
(iii)
4
(iv)
8
(v)
3
Question
6
6.
Find the value of
x
if
log
(
x
+
9
)
+
log
(
x
−
9
)
=
log
2
(i)
(
83
,
(
−
√
83
)
)
(ii)
(
83
,
(
−
83
)
)
(iii)
(
√
83
,
(
−
√
83
)
)
(iv)
(
√
83
,
(
−
83
)
)
Question
7
7.
Find the value of
x
if
log
10
(
x
+
7
)
−
log
10
(
x
−
7
)
=
1
(i)
93
11
(ii)
25
3
(iii)
77
9
(iv)
61
7
(v)
79
9
Question
8
8.
Find the value of
x
if
log
2
(
x
2
−
60
)
=
2
(i)
(
9
,
(
−
8
)
)
(ii)
(
9
,
(
−
7
)
)
(iii)
(
8
,
(
−
7
)
)
(iv)
(
8
,
(
−
8
)
)
Question
9
9.
Solve
log
x
log
9
=
log
81
log
1
9
(i)
(
-1
81
)
(ii)
1
83
(iii)
1
81
(iv)
1
27
(v)
1
79
Question
10
10.
Find the value of
x
if
log
x
125
=
3
(i)
7
(ii)
5
(iii)
4
(iv)
3
(v)
6
Question
11
11.
Find the value of
x
if
log
5
x
=
2
(i)
22
(ii)
24
(iii)
26
(iv)
28
(v)
25
Question
12
12.
Find the value of
x
if
log
2
4
=
x
(i)
5
(ii)
3
(iii)
2
(iv)
(-1)
(v)
1
Question
13
13.
Find the value of
x
if
log
√
4
(
−
x
−
3
)
=
2
(i)
-7
(ii)
-10
(iii)
-6
(iv)
-4
(v)
-8
Question
14
14.
Find the value of
x
if
log
x
1
625
=
-4
(i)
3
(ii)
8
(iii)
4
(iv)
5
(v)
6
Question
15
15.
Find the value of
x
if
log
(
x
+
2
)
+
log
(
x
−
2
)
=
log
4
(i)
(
2
√
2
,
(
−
2
√
2
)
)
(ii)
(
2
√
2
,
(
−
4
)
)
(iii)
(
4
,
(
−
2
√
2
)
)
(iv)
(
4
,
(
−
4
)
)
Question
16
16.
Find the value of
x
if
log
4
(
x
+
6
)
−
log
4
(
x
−
6
)
=
1
(i)
7
(ii)
10
(iii)
13
(iv)
11
(v)
9
Question
17
17.
Find the value of
x
if
log
3
(
x
2
−
16
)
=
2
(i)
(
6
,
(
−
4
)
)
(ii)
(
5
,
(
−
4
)
)
(iii)
(
6
,
(
−
5
)
)
(iv)
(
5
,
(
−
5
)
)
Question
18
18.
Solve
log
x
log
6
=
log
81
log
1
9
(i)
(
-1
36
)
(ii)
1
36
(iii)
1
38
(iv)
1
12
(v)
1
34
Question
19
19.
If
log
(
x
2
+
1
)
log
2
x
2
=
1
, find x
(i)
(
0
,
-1
)
(ii)
(
-1
,
1
)
(iii)
(
-1
,
0
)
(iv)
(
0
,
2
)
(v)
(
2
,
1
)
Question
20
20.
If
log
(
x
2
+
25
)
log
2
x
2
=
1
, find x
(i)
(
-2
,
5
)
(ii)
(
-5
,
5
)
(iii)
(
-5
,
4
)
(iv)
(
-4
,
6
)
(v)
(
4
,
-5
)
Assignment Key
1) (iii)
2) (v)
3) (iv)
4) (v)
5) (ii)
6) (iii)
7) (iii)
8) (iv)
9) (iii)
10) (ii)
11) (v)
12) (iii)
13) (i)
14) (iv)
15) (i)
16) (ii)
17) (iv)
18) (ii)
19) (ii)
20) (ii)
