Question

Solve for x:

`(a/b)^(1 - 2x) = root(3)(b/a)`

Answer 1

Given expression is `(a/b)^(1 - 2x) = root(3)(b/a)`.

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

Thus, `(a/b)^(1 - 2x) = root(3)(b/a)`

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

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

Equating the powers with same bases.

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

3(1 – 2x) = –1

3 – 6x = –1

4 = 6x

`x = 4/6`

`x = 2/3`

Therefore, the value of x in the given expression is `2/3`.