Solution
= Solution
Near zero the logarithm's argument is positive, so $\ln[(2+x)^3]=3\ln(2+x)=3\ln2+3\ln(1+x/2)$. Use the <Maclaurin series> of the <natural logarithm>:
$$
\boxed{\ln[(2+x)^3]=3\ln2+\frac32x-\frac38x^2+\frac18x^3+O(x^4).}
$$
The local calculation uses $x>-2$ for the real logarithm; the <power series> converges for $|x|<2$.