for what values of x, it is not possible to graph the function log (x-1)?

x - 1 > 0
x > 1

Thus it is not possible if x <= 1.

You may also think of it this way:
y = logx is a graph where 0 < x < infinity
If you translate it a unit to the right, it becomes 1 < x < infinity
Thus x > 1
It is not possible to graph if x <= 1