I am trying to say that a single-valued function satisfies the definition of a multi-valued function. For example, if I define the following: $$\newcommand{\Log}{\operatorname{Log}} f(z):=\Log(z)+2\lfloor{|z|}\rfloor\pi i$$ I want to say $f(z)$ is an instance of $\log(z)$ in the sense that $e^{f(z)}=z$.
Are there any symbols or phrases to present this idea? If I just say “$f(z)=\log(z)$”, it would be ambiguous. If I say “$f(z)\in\log(z)$”, that would mean $\log(z)$ is a set. If I say “$f(z)$ is an instance of $\log(z)$”, it will be quite confusing. I can say “$e^{f(z)}=z$” for this example. However, in case I had to define a multi-valued function in a complicated way, I would not want to repeat the definition of that multi-valued function many times.
How to present the idea that “(a single-valued function) is an instance of (a multi-valued function)” in a clear, unambiguous manner?
