Using L'Hopital's Rule to find a log function

Question

Hi, I need help answering this problem.

lim (ln 4x-ln(x+1))

x→∞

Answer 1

You may rewrite your function as f(x)=ln[(4x)/(x+1)] or e^{f(x)}=(4x)/(x+1). The limit of the RHS as x goes to infinity is equal to 4. Hence, lim f(x) as x goes to infinity equals to ln4.