Answer
diverges toward $-\infty$
Work Step by Step
In the proof of Th.5.1. we noted that
as $t\rightarrow 0^{+}$ (t approaches 0 from the right)
then ln(t)$\rightarrow-\infty$ (diverges toward $-\infty$).
(see fig.5.3)
Here, if we set $\mathrm{t}=6-x$, and
when $x\rightarrow 6^{-},$then $t\rightarrow 0^{+}$,
(from the right, because we are subtracting a number smaller than 6 from 6)
so we can write
$\displaystyle \lim_{x\rightarrow 6^{-}}\ln( 6-x)=\displaystyle \lim_{t\rightarrow 0^{+}}\ln t=-\infty$
