Limit Problem 2

$\begin{aligned} L & = \lim _{x \to 1} \frac 3{x-1}\left( \ln(x^5)+ \frac 1x - e^{\ln (x^6)} \right) \\ &= \lim _{x \to 1} \frac {3\left (5\ln x +\frac 1x-x^6\right) }{x-1} & \small \color{#3D99F6} \text {A 0/0 case, L'Hôpital rule applies.} \\ &= \lim _{x \to 1} \frac {3\left ( \frac 5x -\frac 1{x^2}-6x^5 \right) }{1} & \small \color{#3D99F6} \text {Differentiate up and down w.r.t. }x \\ &= 3(5-1-6) = \boxed{-6} \end{aligned}$