Question

Solve for x:

`(625)^(x - 1) = (0.008)^(3 - x)`

Answer 1

Given expression is `(625)^(x - 1) = (0.008)^(3 - x)`.

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

Thus, 

`(625)^(x - 1) = (0.008)^(3 - x)`

`(5^4)^(x - 1) = (8/1000)^(3 - x)`

`(5^4)^(x - 1) = (2^3/10^3)^(3 - x)`

`(5)^(4x - 4) = (2/10)^(3(3 - x))`  ...`[a^n/b^n = (a/b)^n]`

`(5)^(4x - 4) = (1/5)^(9 - 3x)`

`(5)^(4x - 4) = (5^-1)^(9 - 3x)`

`(5)^(4x - 4) = (5)^(-1(9 - 3x))`

`(5)^(4x - 4) = (5)^(3x - 9)`

Equating the powers with same bases.

4x – 4 = 3x – 9

4x – 3x = 4 – 9

x = –5

Hence, the value of x in given expression is –5.