UX Movement does a fair job of giving an overview of the downsides to many Sign Up / Log In combinations. I’ve long tried to avoid this conundrum by simply making the “sign up” action more descriptive.
The bottom line: don’t be lazy. Focus on an action, “Start Sharing”, “Open A Store”, or at worst, as UX Movement suggests, “Create Account”. “Sign Up” just isn’t good enough anymore, we can do better.