Part of the "One account, all of Google" thing we wrote about recently is that it brings all of your services and data together on your android device once you log in.
But sometimes, you don't need all of your accounts on all of your apps. Such as Google+. I have a professional account (well, professional-looking account, anyway), and all I do with it is apply for jobs. I don't need it in Google+, I only need it in Gmail, and so, I'm logging it out of Google+. Or maybe your business uses Google Apps, and so you've got a superfluous Google+ account with it, too.
Here's how you can silence that second account forever, without actually deleting it.
First, we enter the settings. Now, I have two accounts (blurred to protect, well, me), and I select the one I'd like to log out of.
At the bottom, below all the account settings, is a simple looking 'Log out' button. You shouldn't have to scroll far, but it may not be immediately visible. And once you click it, you're logged out. No "are you sure?" popup, it just works for a second and the account vanishes from the list. If you wish to add the account, or any other, back in, there's a log-in button in that same place.
That's it. Peace and quiet awaits.