Question

Solve for x:

`sqrt((3/4)^(1 - 3x)) = 2 10/27`

Answer 1

Given expression is `sqrt((3/4)^(1 - 3x)) = 2 10/27`.

We have to find the value of x in given expression.

Thus, `sqrt((3/4)^(1 - 3x)) = 2 10/27`

`[(3/4)^(1 - 3x)]^(1/2) = 64/27`  ...`[∴ root(n)(a) = a^(1/n)]`

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

`(3/4)^((1 - 3x)/2) = (4/3)^3`  ...`[∴ (a^n)^m = a^(nm)]`  

`(3/4)^((1 - 3x)/2) = (3/4)^-3`  ...`[∴ (a/b)^n = (b/a)^-n]`

Equating the powers with same bases.

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

1 – 3x = –3 × 2

1 – 3x = –6

1 + 6 = 3x

7 = 3x

⇒ `x = 7/3`

Therefore, the value of x in given expression is `7/3`.