abstract algebra - Uniqueness of the endomorphism of the multiplicative group of positive real numbers

How do we prove that the endomorphism of the multiplicative group of positive real numbers is unique (up to a complex variable)!? meaning: how do we prove that it has the following - and only the following - form:
$$f(x)=x^{s}\;\;\;\;(x\in \mathbb{R}^{+} \;\;,s\in\mathbb{C})$$