Hello, I was able to do part one but have problem finding the domain

f(x) = x / [1-ln(x-1)]

The solution says:

x<=1 and ln(x-1) = 1

x<=1 and ln(x-1) = ln e

x<=1 and x-1 = ln e

--> Here I do not understand how to get from ln(x-1) to x-1

x<=1 and x = (e + 1) --> I do not get this step too

Can someone explain that to me. Thanks