# How do you solve ln [((x+1) / x)]=1?

May 2, 2018

$x = \frac{1}{e - 1}$

#### Explanation:

We have:

$\ln \left(\frac{x + 1}{x}\right) = 1$

Therefore, by the definition of the logarithm, we have:

$\frac{x + 1}{x} = e$

Which we now solve for $x$:

$x + 1 = e x$

$\therefore \left(e - 1\right) x = 1$

Giving the solution:

$x = \frac{1}{e - 1}$