161
Chapter 4
Exercises 4.1
1.
4
x
=
(2
2
)
x
=
2
2
x
,
1/ 2
(1/ 2)
(
3)
(3
)
3
x
x
x
=
=
,
1
9
⎛
⎝
⎜
⎞
⎠
⎟
x
=
(9
−
1
)
x
=
((3
2
)
−
1
)
x
=
3
−
2
x
2.
27
x
=
(3
3
)
x
=
3
3
x
,
1/ 3
(1/ 3)
3
(
2)
(2
)
2
x
x
x
=
=
,
1
8
⎛
⎝
⎜
⎞
⎠
⎟
x
=
(8
−
1
)
x
=
((2
3
)
−
1
)
x
=
2
−
3
x
3.
8
2
x
/3
=
(2
3
)
2
x
/3
=
2
3(2
x
/3)
=
2
2
x
,
9
3
x
/ 2
=
(3
2
)
3
x
/2
=
3
2(3
x
/2)
=
3
3
x
,
16
−
3
x
/ 4
=
(2
4
)
−
3
x
/ 4
=
2
4(
−
3
x
/ 4)
=
2
−
3
x
4.
9
−
x
/2
=
(3
2
)
−
x
/2
=
3
2(
−
x
/2)
=
3
−
x
,
8
4
x
/3
=
(2
3
)
4
x
/ 3
=
2
3(4
x
/3)
=
2
4
x
,
27
−
2
x
/3
=
(3
3
)
−
2
x
/3
=
3
3(
−
2
x
/3)
=
3
−
2
x
5.
1
4
⎛
⎝
⎜
⎞
⎠
⎟
2
x
=
(4
−
1
)
2
x
=
((2
2
)
−
1
)
2
x
=
2
−
4
x
,
1
8
⎛
⎝
⎜
⎞
⎠
⎟
−
3
x
=
(8
−
1
)
−
3
x
=
((2
3
)
−
1
)
−
3
x
=
2
9
x
,
1
81
⎛
⎝
⎜
⎞
⎠
⎟
x
/2
=
(81
−
1
)
x
/ 2
=
((3
4
)
−
1
)
x
/2
=
3
−
2
x
6.
1
9
⎛
⎝
⎜
⎞
⎠
⎟
2
x
=
(9
−
1
)
2
x
=
((3
2
)
−
1
)
2
x
=
3
−
4
x
,
1
27
⎛
⎝
⎜
⎞
⎠
⎟
x
/3
=
(27
−
1
)
x
/3
=
((3
3
)
−
1
)
x
/3
=
3
−
3(
x
/3)
=
3
−
x
1
16
⎛
⎝
⎜
⎞
⎠
⎟
−
x
/2
=
(16
−
1
)
−
x
/2
=
((2
4
)
−
1
)
−
x
/2
=
2
−
4(
−
x
/2)
=
2
2
x
7.
6
x
⋅
3
−
x
=
(2
⋅
3)
x
⋅
3
−
x
=
2
x
⋅
(3
x
⋅
3
−
x
)
=
2
x
⋅
(3
x
−
x
)
=
2
x
,
15
x
5
x
=
(3
⋅
5)
x
5
x
=
3
x
⋅
5
x
5
x
=
3
x
,
12
x
2
2
x
=
(3
⋅
4)
x
2
2
x
=
3
x
⋅
4
x
2
2
x
=
3
x
⋅
(2
2
)
x
2
2
x
=
3
x
8.
7
−
x
⋅
14
x
=
7
−
x
⋅
(7
⋅
2)
x
=
7
−
x
⋅
7
x
⋅
2
x
=
7
−
x
+
x
⋅
2
x
=
2
x
2
x
6
x
=
2
(2
⋅
3)
x
=
2
x
2
x
⋅
3
x
=
1
3
x
=
3
−
x
3
2
x
18
x
=
3
2
x
9
x
⋅
2
x
=
3
2
x
3
2
x
⋅
2
x
=
1
2
x
=
2
−
x
9.
3
4
x
3
2
x
=
3
4
x
⋅
3
−
2
x
=
3
4
x
−
2
x
=
3
2
x
,
2
5
x
+
1
2
⋅
2
−
x
=
2
5
x
+
1
2
1
−
x
=
2
5
x
+
1
⋅
2
−
(1
−
x
)
=
2
5
x
+
1
−
(1
−
x
)
=
2
6
x
,
9
−
x
27
−
x
/3
=
(3
2
)
−
x
(3
3
)
−
x
/3
=
3
−
2
x
3
−
x
=
3
−
2
x
⋅
3
x
=
3
−
2
x
+
x
=
3
−
x
10.
2
x
6
x
=
2
x
(2
⋅
3)
x
=
2
x
2
x
⋅
3
x
=
1
3
x
=
3
−
x
,
3
−
5
x
3
−
2
x
=
3
−
5
x
⋅
3
2
x
=
3
−
5
x
+
2
x
=
3
−
3
x
,
16
x
8
−
x
=
(2
4
)
x
(2
3
)
−
x
=
2
4
x
⋅
2
3
x
=
2
4
x
+
2
x
=
2
7
x
11.
2
3
x
⋅
2
−
5
x
/ 2
=
2
3
x
−
(5
x
/2)
=
2
(6
x
/2)
−
(5
x
/2)
=
2
x
/ 2
,
3
2
x
⋅
1
3
⎛
⎝
⎜
⎞
⎠
⎟
2
x
/ 3
=
3
2
x
⋅
(3
−
1
)
2
x
/3
=
3
2
x
⋅
3
−
2
x
/3
=
3
(6
x
/3)
−
(2
x
/3)
=
3
4
x
/3
=
3
(4/3)
x
12.
2
5
x
/4
⋅
1
2
⎛
⎝
⎜
⎞
⎠
⎟
x
=
2
5
x
/4
⋅
(2
−
1
)
x
=
2
5
x
/ 4
⋅
2
−
4
x
/4
=
2
(5
x
/4)
−
(4
x
/ 4)
=
2
x
/4
,
3
−
2
x
⋅
3
5
x
/2
=
3
−
4
x
/2
⋅
3
5
x
/2
=
3
(
−
4
x
/2)
+
(5
x
/ 2)
=
3
x
/2
13.
(2
−
3
x
⋅
2
−
2
x
)
2/5
=
(2
−
3
x
−
2
x
)
2/5
=
(2
−
5
x
)
2/ 5
=
2
−
2
x
,
(9
1/ 2
⋅
9
4
)
x
/ 9
=
((3
2
)
1/2
⋅
(3
2
)
4
)
x
/9
=
(3
1
⋅
3
8
)
x
/9
=
(3
1
+
8
)
x
/ 9
=
(3
9
)
x
/9
=
3
x
14.
(3
−
x
⋅
3
x
/5
)
5
=
3
−
5
x
⋅
3
(
x
/5)5
=
3
−
5
x
⋅
3
x
=
3
−
5
x
+
x
=
3
−
4
x
,
(16
1/4
⋅
16
−
3/4
)
3
x
=
((2
4
)
1/ 4
⋅
(2
4
)
−
3/4
)
3
x
=
(2
1
⋅
2
−
3
)
3
x
=
(2
1
−
3
)3
x
=
(2
−
2
)
3
x
=
2
−
6
x

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