Đề bài

Tìm số tự nhiên x, biết: a)     225: 15 + 3.(2x +1) = 270;

b)    19.(2+3+4-5+6-7)² – 9.(7x – 2) =0;

c)     3.(2x +1)³ = 81;

d)    (x+1)⁵ = 243;

e)     2.11^x = (3²+2)³ : (5³ – 2⁵:2³).22;

g) 7^x+7^x+1+7^x+2=3.19.343.

Lời giải chi tiết

a)     225: 15 + 3.(2x +1) = 27015 + 3.(2x+1) = 2703.(2x+1) = 270 – 153.(2x+1) = 2552x+1 = 255:32x+1 = 852x = 84x = 42Vậy x =42 

b)    19.(2+3+4-5+6-7)² – 9.(7x – 2) =0

19. 3² – 9.(7x -2) = 0

19.9 – 9.(7x – 2) = 09. [19 – (7x – 2)] = 019 – (7x – 2) = 019 = 7x – 27x = 21x =3Vậy x=3

c)     3.(2x +1)³ = 81

(2x + 1)³ = 81:3=27

(2x+1)³ = 3³

2x+1  = 32x =2x =1Vậy x = 1

d)    (x+1)⁵ = 243

(x+1)⁵ = 3⁵

x +1 = 3x = 2Vậy x = 2

e)     2.11^x = (3²+2)³ : (5³ – 2⁵:2³).22

2.11^x = 11³ : (5³ - 2²) .22

2.11^x = 11³ : (125 – 4).22

2.11^x = 11³ : 121.22

2.11^x = 11³ : 11².22

2.11^x = 11. 11. 2

2.11^x = 11².2

11^x = 11²

x = 2Vậy x =2

g) 7^x+7^x+1+7^x+2=3.19.343.

7^x+ 7. 7^x + 7².7^x = 57.343

7^x . (1+7+7²) = 57 . 7³

7^x . 57 =57 . 7³

7^x = 7³

x = 3Vậy x= 3