1

65 63
x
32
= 4 or 0. 0625
When x 4
3 4 4 5 3
6 9 3
3 =3
Since the LHS = RHS.
Hence it satisfies the equation.
When x 0. 0625
3 0.0625 0.0625 5 3
0.75 – 2.25 ≠ 3Does not satisfy
Hence x 4 .
Example 3 Solve the following equation,
verify your solutions in each case.
(i) 2x
1
x x 3
(ii)
Solution:
x 6 4 x 1
3x
(i) 2x
1
x x 3
2x
1
x 2 x 3 2
x 1
x 2 x 2x
1
x
3x
1 x
3 2 x2x
1
2 3
2
2x
4 2 2 x2x
1
4x
2 16
x 16
4x
2x
1
2
4x 16x
16
8x
4x
4x
2 12x 16
0
12
x
12
12 20
x
8
x 4 or -1
2
2
4
416
8
When x = -1, 1
1
4
Does not satisfy
When x 4
8 1 – 4 = 4 3
3 – 2 = 1 Satisfies
x 4
(ii)
x 6 4 x 1
3x
2
x 6 4 x 1
3x
2
x 6
4
x
2 x
64
x 1
3x
2 x 64
x 10
1
3x
2 x
64
x 3x
9
2 x
64
x 2
3x
9 2
2
4x 64
x 9x
81 54x
2
2
x x 24 6x
9x
54 x 81
4 4
8x
4x
2
96 9x
13x
2 62 x 15
0
2
54x
81
62 62 13
415
x
213
62 68
=
26
6
= or 5
26
3
= or 5
13
When x 5
we will have
2
5 6 4
5 1
15
1 9 16
13
4 it Satisfies
3
When x we will have
13
3
13
6
81
13
9
4
49
13
7
3
13
2
4
13
13 13 13
16 2
13 13
16 2 Does not satisfy
Hence x = -5 only.
1
3
13