`4) (3/2)^(x - 1) + (3/2)^(x + 1) = 117/16`

`to (3/2)^(x - 1) + (3/2)^(x - 1) . (3/2)^2 = 117/16`

`to (3/2)^(x - 1) + (3/2)^(x - 1) . 9/4 = 117/16`

`to (3/2)^(x - 1) . (1 + 9/4) = 117/16`

`to (3/2)^(x - 1) . 13/4 = 117/16`

`to (3/2)^(x - 1) = 9/4`

`to (3/2)^(x - 1) = (3/2)^2`

`to x - 1 = 2`

`to x = 3`

Vậy `x = 3`

`5) (1/5)^(x - 2) + (1/5)^(x - 1) = 6/25`

`to (1/5)^(x -2) + (1/5)^(x - 2) . 1/5 = 6/25`

`to (1/5)^(x - 2) . (1 + 1/5) = 6/25`

`to (1/5)^(x - 2) . 6/5 = 6/25`

`to (1/5)^(x - 2) = 1/5`

`to (1/5)^(x - 2) = (1/5)^1`

`to x - 2 = 1`

`to x = 3`

Vậy `x = 3`

`6) (2/7)^(x - 3) - (2/7)^(x - 2) = 10/49`

`to (2/7)^(x - 3) - (2/7)^(x - 3) . 2/7 = 10/49`

`to (2/7)^(x - 3) . (1- 2/7) = 10/49`

`to (2/7)^(x - 3) . 5/7 = 10/49`

`to (2/7)^(x - 3) = 2/7`

`to (2/7)^(x - 3) = (2/7)^1`

`to x - 3 = 1`

`to x = 4`

Vậy `x = 4`