Question

Solve for x:

`root(3)((25/49)^(x - 1)) = 2 93/125`

Answer 1

Given expression is `root(3)((25/49)^(x - 1)) = 2 93/125`.

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

Thus, `root(3)((25/49)^(x - 1)) = 2 93/125`

`[(25/49)^(x - 1)]^(1/3) = 343/125`   ...`[∴ root(n)(a) = a^(1/n)]`

`[(5^2/7^2)^(x - 1)]^(1/3) = 7^3/5^3`

`[(5/7)^(2x - 2)]^(1/3) = (7/5)^3`  ...`[∴ (a^n)^m = a^(nm)]`

`[5/7]^((2x - 2)/3) = [5/7]^-3`  ...`[∴ (a/b)^n = (b/a)^-n]`

Equating the powers with same bases.

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

2x – 2 = –3 × 3

2x – 2 = –9

2x = –9 + 2

2x = –7

⇒ `x = (-7)/2`

Therefore, the value of x in the given expression is `(-7)/2`.