Asked by Brenda
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?
Answers
Answered by
oobleck
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|
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|
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.