[tex]f(x) = \ln(2x+3)[/tex]
[tex]f'(x) = \dfrac{(2x+3)'}{2x+3} = \dfrac{2}{2x+3}[/tex]
[tex]\lim\limits_{x\to 3}\dfrac{f(x)-f(3)}{x-3}\overset{\frac{0}{0}(L'H.)}{=} \lim\limits_{x\to 3}\dfrac{\left[f(x)-f(3)\right]'}{(x-3)'}=[/tex]
[tex]= \lim\limits_{x\to 3}\dfrac{f'(x) - 0}{1-0} = \lim\limits_{x\to 3}f'(x) = f'(3) = \dfrac{2}{2\cdot 3+3} =[/tex]
[tex]= \boxed{\dfrac{2}{9}}[/tex]
