Iterative function $f^i(n)=3n$ where $n\in\mathbb{N} \setminus \{ 2^i \}$ never reaches $2^x$

Question

Iterative Function $f^i(n)=3n$, where $x\in\mathbb{N}$ and $n\in\mathbb{N} \setminus \{ 2^x \}$ as $x\to\infty$.

How can we show that $f^i(n)$ as $i\rightarrow \infty$, never reaches $2^i$. The question is how to prove that $f^i$ never reaches a power of two number when the initial input $n$ is not in the set of power of two numbers.