limit as x approaches 1, ln(x-1)

You need to know what a log graph looks like.

  $$\\\lim_{x\rightarrow +0}\;\;lnx=-\infty\\ so\\ \lim_{x\rightarrow +1}\;\;ln(x-1)=-\infty\\\\ because \;x-1=0 \;when \;x=1$$