What is the domain of ln(x-2)^2 and what does the graph look like. I have tried a couple of different graphing tools and there is nothing to the left of the vertical asymptote. However, one graphing tool shows a reflected image across the vertical asymptote. Which is correct and why?

Question

What is the domain of ln(x-2)^2 and what does the graph look like. I have tried a couple of different graphing tools and there is nothing to the left of the vertical asymptote.  However, one graphing tool shows a reflected image across the vertical asymptote.  Which is correct and why?

oobleck · Accepted Answer

the domain of lnx is x>0
so the domain if ln(x-2) is x-2 > 0, or x > 2
Now, if you use
ln(x-2)^2 = 2 ln(x-2) then you get the domain above.

If you use ln (x-2)^2 then since it is always positive except for x=2, then the domain is all real numbers except x=2
That is equivalent to 2 ln|x-2|