We now have

lim$$x $$ $(8$x $$ ln$($x$))=$lim$$x $$ $8$x

$1$

ln$($x$)8$x

$.$

Let's first focus on

lim$$x $$ $$

ln$($x$)8$x

$.$

Since

ln$($x$)$

as

x $$ $,$

then this limit is indeterminate of type $/$$.$

Using l'Hospital's Rule, we find:

lim$$x $$ $$

ln$($x$)8$x

$=$lim$$x $$