A useful property of the logarithm is that it can "convert" multiplication into addition, as in
$\text{ln}(a)+\text{ln}(b)=\text{ln}(ab) \text{ for all } a, b \in \mathbb{R}^+$$\ln(a)+\ln(b)=\ln(ab) \text{ for all } a, b \in \mathbb{R}^+$
Does there exist a function $f$, which holds a similar property for exponentiation?
$f(a)+f(b)=\text{f}(a^b) \text{ for all } a, b \in \mathbb{R}^+$$f(a)+f(b)=f(a^b) \text{ for all } a, b \in \mathbb{R}^+$
If so, are there any closed-form expressions for such a function?
