Solution
= Solution
The <complex number> $\sqrt3+i$ has <modulus> two and <principal argument> $\pi/6$. Therefore its <principal complex logarithm> is
$$
\boxed{\operatorname{Log}(\sqrt3+i)=\ln2+i\frac\pi6.}
$$
If the source's logarithm means the full multivalued <complex logarithm>, rather than its principal value, the complete answer is $\ln2+i(\pi/6+2\pi n)$ with $n\in\mathbb Z$. A branch convention is necessary to obtain a unique imaginary part.