Sometimes I encounter difficulties signing out of an account on Amazon's website when I need to sign into another account, if the resolution of the display isn't great enough to allow me to see the bottom of Amazon's list of choices where the sign out option appears. If I need to logon on such a system, there's no problem. If I visit Amazon's home page, I can click on "Hello. Sign in Accounts & Lists" where I see a "Sign in" button.
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