\(\lim\limits_{x\to2}\,\,\, \frac{x-2}{log(x-1)}\) [\(\frac00-case\)]
= \(\lim\limits_{x\to2}\,\, \cfrac{1}{\frac{1}{x-1}}\) [By using D.L.H Rule]
= \(\lim\limits_{x\to2}\,\,\,(x-1)\)
= 2 - 1 = 1
\(\therefore\) \(\lim\limits_{x\to2}\,\,\, \frac{x-2}{log(x-1)}=1\)
