How do you sketch the graph of #y=log_2(x-1)#?
It is the graph of log base 2, with a horizontal translation of 1 unit right.
To graph how to graph
From that graph, the value of k is -1, which means that the graph of log base 2 is translated 1 unit right.
Also note that due to this translation, the vertical asymptote is translated 1 unit left, and would then become x=1.