Bài 2:

a) (x - 29) - 11 = 0

⇔ x - 29 = 0 + 11

⇔ x - 29 = 11

⇔ x = 11 + 29

⇔ x = 40

Vậy x = 40

b) 531 - (312 - x) + 15 = 246

⇔ 531 - (312 - x) = 246 - 15

⇔ 531 - (312 - x) = 231

⇔ 312 - x = 531 - 231

⇔ 312 - x = 300

⇔ x = 312 - 300

⇔ x = 12

Vậy x = 12

c) (4x + 5) : 3 - 121 : 11 = 4

⇔ (4x + 5) : 3 - 11 = 4

⇔ (4x + 5) : 3 = 4 + 11

⇔ (4x + 5) : 3 = 15

⇔ 4x + 5 = 15 . 3

⇔ 4x + 5 = 45

⇔ 4x =45 - 5

⇔ 4x = 40

⇔ x = 40 : 4

⇔ x = 10

Vậy x = 10

d) 131x - 941 = $2^{7}$ . $2^{3}$

⇔ 131x - 941 = $2^{7 + 3}$

⇔ 131x - 941 = $2^{10}$

⇔ 131x - 941 = 1024

⇔ 131x = 1024 + 941

⇔ 131x = 1965

⇔ x = 1965 : 131

⇔ x = 15

Vậy x = 15

e) 225 : 15 + 3 . (2x + 1) = 270

⇔ 15 + 3 . (2x + 1) = 270

⇔ 3 . (2x + 1) = 270 - 15

⇔ 3 . (2x + 1) = 255

⇔ 2x + 1 = 255 : 3

⇔ 2x + 1 = 83

⇔ 2x = 83 - 1

⇔ 2x = 82

⇔ x = 82 : 2

⇔ x = 41

Vậy x = 41

f) 19 . $(2 + 3 + 4 - 5 + 6 - 7)^{2}$ - 9 . (7x - 2) = 0

⇔ 19 . $3^{2}$ - 9 . (7x - 2) = 0

⇔ 19 . 9 - 9 . (7x - 2) = 0

⇔ 171 - 9 . (7x - 2) = 0

⇔ 9 . (7x - 2) = 171 - 0

⇔ 9 . (7x - 2) = 171

⇔ 7x - 2 = 171 : 9

⇔ 7x - 2 = 19

⇔ 7x = 19 + 2

⇔ 7x = 21

⇔ x = 21 : 3

⇔ x = 7

Vậy x = 7

g) 3 . $(2x + 1)^{3}$ = 81

⇔ $(2x + 1)^{3}$ = 81 : 3

⇔ $(2x + 1)^{3}$ = 27

⇔ $(2x + 1)^{3}$ = $3^{3}$

⇒ 2x + 1 = 3

⇔ 2x = 3 - 1

⇔ 2x = 2

⇔ x = 2 : 2

⇔ x = 1

Vậy x = 1

h) $(x + 1)^{5}$ = 243

⇔ $(x + 1)^{5}$ = $3^{5}$

⇒ x + 1 = 3

⇔ x = 3 - 1

⇔ x = 2

Vậy x = 2

i) 2 . $11^{x}$ = $(3^2 + 2)^{3}$ : ($5^{3}$ - $2^{5}$ : $2^{3}$) . 22

⇔ 2 . $11^{x}$ = $(9 + 2)^{3}$ : (125 - 4) . 22

⇔ 2 . $11^{x}$ = $11^{3}$ : 121 . 22

⇔ 2 . $11^{x}$ = $11^{3}$ : $11^{2}$ . 22

⇔ 2 . $11^{x}$ = 11 . 22

⇔ 2 . $11^{x}$ = 242

⇔ $11^{x}$ = 242 : 2

⇔ $11^{x}$ = 121

⇔ $11^{x}$ = $11^{2}$

⇒ x = 2

Vậy x = 2

k) $7^{x}$ +  $7^{x+1}$ +  $7^{x+2}$ = 3 . 19 . 343

⇔ $7^{x}$ +  $7^{x+1}$ +  $7^{x+2}$ = 19551

⇔ $7^{x}$ + $7^{x+1}$ . $7^{1}$ + $7^{x+2}$ . $7^{2}$ = 19551

⇔ $7^{x}$ . (1 + $7^{1}$ + $7^{2}$) = 19551

⇔ $7^{x}$ . (1 + 7 + 49) = 19551

⇔ $7^{x}$ . 57 = 19551

⇔ $7^{x}$ = 19551 : 57

⇔ $7^{x}$ = 343

⇔ $7^{x}$ = $7^{3}$

⇒ x = 3

Vậy x = 3

Bài 4:

a) (1 . 3 . 5 . 7 .9) `\vdots` 5; 20 `\vdots` 5

⇒ A `\vdots` 5; A > 5. Vậy A là hợp số.

b) (21 . 22 . 23) `\vdots` 7; (6 . 7 . 8) `\vdots` 7

⇒ B `\vdots` 7; A > 7. Vậy B là hợp số.