Hello!
The parent function, y = ln(x), has a vertical and horizontal translation.
y = ln(x - h) + k | In this equation, h is the vertical shift, and k is the horizontal shift.
If ln(x - k), then the graph is translated right k units.
If ln(x + k), then the graph is translated left k units.
If ln(x) + h, then the graph is translated up h units.
If ln(x) - h, then the graph is translated down h units.
Therefore, the graph of y = ln(x - 7) + 3 is translated 3 units up and 7 units to the right, which is choice D.