Injective functions $f : \mathbb{R} \rightarrow\mathbb{R}$, such that for any $x, y \in \mathbb{R}$, they satisfy the condition $f(xy) = f(f(x)f(y))$.

Find all injective functions $f : \mathbb{R} \rightarrow \mathbb{R}$, such that for any $x, y \in \mathbb{R}$, they satisfy the condition: $f(xy) = f(f(x)f(y))$.

Attempt: Because f is injective, $xy=f(x)f(y)$. What now?