at the point x = 8 together with the graph of this function.
Using Maple:
> f:=x->ln(x-6);
> a:=8;
> m:=limit((f(a+h)-f(a))/h,h=0);
> g:=x->m*(x-a)+f(a);
> plot({f(x),g(x)},x=6..10);