Tao wrote in his blog post (in the fourth last paragraph):
Thus we see that any proposed proof of the Collatz conjecture must either use transcendence theory, or introduce new techniques that are powerful enough to create exponential separation between powers of $2$ and powers of $3$.
What does he exactly mean about "exponential separation between powers of $2$ and powers of $3$"?
Are there any simple explanations or examples that can be shown?