solve the following limit,
limit when x approaches 0 from the positive direction
ln(4x)
first note that $\displaystyle \ln4x=\ln4+\ln x$ so we'll worried about the $\displaystyle \ln x.$
now consider $\displaystyle x=\frac19,$ or $\displaystyle \frac1{99}$ and so on.
for small enough $\displaystyle x$ then using the fact that $\displaystyle \ln\frac1a=-\ln a$ yields the answer i gave.
take a moment and think it for a while.