Question

How do you sketch the graph of `y=log_2(x-1)`?

Answer 1

It is the graph of log base 2, with a horizontal translation of 1 unit right.

Explanation:

To graph how to graph `y=log2x` , you could always change it to an exponential equation, which would be `2^y=x` and pick some values of y to find x values. This would give you the 'original' 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.