a)(1/3)^x+3+(1/3)^x+2=4/27

b)(2/3)^x+2+(2/3)^x+1=20/27

c) (3x-2)^2=49/81

d) (1-5x)^3=1/27

( Giúp e vs ạ)

Đáp án + Giải thích các bước giải:

`a. \frac{1}{3}^{x + 3}+ \frac{1}{3}^{x + 2} = 4/27`

`\frac{1}{3}^{x + 2} . (1/3)^1 + \frac{1}{3}^{x + 2} = 4/27`

`\frac{1}{3}^{x + 2}. (1/3 + 1) = 4/27`

`\frac{1}{3}^{x} . 4/3 = 4/27`

`\frac{1}{3}^{x} = 4/27 : 4/3`

`\frac{1}{3}^{x} = 1/9`

`\frac{1}{3}^{x} = (1/3)^2`

`x = 2`

`Vậy  x = 2`

`b. \frac{2}{3}^{x + 2}+ \frac{2}{3}^{x + 1} = 20/27`

`\frac{2}{3}^{x} . (2/3)^2 + \frac{2}{3}^{x} . 2/3= 20/27`

`\frac{2}{3}^{x} . 4/9 + \frac{2}{3}^{x} . 2/3= 20/27`

`\frac{2}{3}^{x}. (4/9 + 2/3) = 20/27`

`\frac{2}{3}^{x} . 10/9 = 20/27`

`\frac{2}{3}^{x} = 20/27 : 10/9`

`\frac{2}{3}^{x} = 2/3`

`\frac{2}{3}^{x} = (2/3)^1`

`x = 1`

`Vậy  x = 1`

`c. (3x - 2)^2 = 49/81`

`(3x - 2)^2 = (7/9)^2   hoặc   (3x - 2)^2 = (-7/9)^2`

`3x - 2 = 7/9                             3x - 2 = -7/9`

`3x = 7/9 + 2                            3x = -7/9 + 2`

`3x = 25/9                                 3x = 11/9`

`x = 25/9 : 3                              x = 11/9 : 3`

`x = 25/27                                  x = 11/27`

`Vậy  x ∈ {25/27;11/27}`

`d. (1 - 5x)^3 = 1/27`

`(1 - 5x)^3 = (1/3)^3`

`1 - 5x = 1/3`

`5x = 1 - 1/3`

`5x = 2/3`

`x = 2/3 : 5`

`x = 2/15`

`Vậy  x = 2/15`