Question

Solve for x:

`125^(x - 1) = 25^(x + 2) xx (625)^(x - 1)`

Answer 1

Given expression is `125^(x - 1) = 25^(x + 2) xx (625)^(x - 1)`.

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

Thus, `125^(x - 1) = 25^(x + 2) xx (625)^(x - 1)`

`(5^3)^(x - 1) = (5^2)^(x + 2) xx (5^4)^(x - 1)`

`(5)^(3x - 1) = (5)^(2x + 2) xx (5)^(4x - 1)` 

`(5)^(3x - 3) = (5)^(2x + 4) xx (5)^(4x - 4)`  ...[∴ (aⁿ)^m = a^nm]

`(5)^(3x - 3) = (5)^(2x + 4 + 4x - 4)`  ...[∴ aⁿ × a^m = a^{n + m}]

`(5)^(3x - 3) = (5)^(6x)`

Equating the powers with same bases.

3x – 3 = 6x

–3 = 6x – 3x

–3 = 3x

x = –1

Therefore, the value of x in given expression is –1.