The domain of a function is the set of all possible #x# values that it is defined for, and the range is the set of all possible #y# values. To make this more concrete, I'll rewrite this as:
#y=ln(x-1)#
Domain: The function #lnx# is defined only for all positive numbers. This means the value we're taking the natural log (#ln#) of (#x-1#) has to be greater than #0#.
Our inequality is as follows:
#x-1>0#
Adding #1# to both sides, we get:
#x>1# as our domain.
To understand the range, let's graph the function #y=ln(x-1)#.
graph{ln(x-1) [-10, 10, -5, 5]}
When we look at our graph, there are no discontinuities in it, thus our range is:
#yinRR#, which just means #y# is a member of the real numbers or #y# can take on any value.
