To log out of the RPR iOS mobile application, click on the settings icon in the upper left-hand corner of the Homepage that looks like a gear. This opens up the options for adjusting your settings and the option to log out as shown below.
You can also tap on "Access to RPR." Below the email and password, see a button that says "Log Out." Tapping this button exits you from the application. The "Access to RPR from this app is set to expire on..." shows the date that the app will automatically log you out and require you to sign back in, due to security considerations.