Question

Question #10661

Answer 1

The value of `x` is `x= (2e^3)/(e^3 - 1)`

Explanation:

Yes you are correct about the first step. Now recall that `ln` and `e` are inverses.

`e^(ln(x/(x- 2))) = e^3`

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

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

`1/e^3 = x/x - 2/x`

`2/x = 1 - 1/e^3`

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

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

Hopefully this helps!