Start by figuring out how the login button relates to other controls in your app.
- How often will it be used relative to other functions?
- How important is it to the user relative to other functions?
- Is there a functional group it could belong to (eg settings or accounts)
- What is the feature density of your app? If you have a lot of menus and buttons you may want to create some menu hierarchy.
Often for mobile apps, the result of this process is that the logout button gets moved off the main menu into an account or settings menu.
The reason is, users usually don't need to log out very often so it's far more valuable to use the screen real estate for more frequently used features.
This is NOT always the case. There are many apps where a login button needs to be easily accessible for security (eg banking), privacy (eg swingers), social (eg user may have multiple gaming accounts) or other reasons.
A proper analysis of the frequency, importance, and taxonomy of your login function relative to all your app functions should result in a pretty clear direction for where to place the button.