which  graph represents the logarithmic function? y=−2ln(x−1)+1

The graph that best represents the function can be seen in the attached graph. What you should do is evaluate a large number of points in the function and find the result. Then graph. Remember that for x = 1 the LN of 0 is not defined since it tends to infinity.

The coordinates of point a right now is (-3,-1) you have to multiply these coordinates by a factor of 2 to get (-6,-2)