I'm reading some notes for an electrical engineering class and came to the following: "...$2^j$ can represent a countably infinite number of real numbers. These examples are related to the fact that if we define w = log(z) to mean that $z=e^w$, then for $z \neq 0$, this logarithm function log(z) is multi-valued."
In here, I was wondering what they mean by multi-valued. There is no further description of this function on the text. Are they referring to the complex logarithmic function? Is the non-complex logarithmic function multi-valued too?