Question

Solve for `x`, given `x^((log_5 x)-2) = (x^2/(125))` ?

Answer 1

`x = {5,125}`

Explanation:

Applying `log_5` to both sides

`(log_5 x-2)log_5 x=2log_5x - 3` and now calling `y = log_5 x`

`(y-2)y=2 y-3` or `y^2-4y+3=0` now solving for `y`

`y = {1,3}` or

`log_5 x = 1 rArr x = 5` and `log_5 x = 3 rArr x = 125`