This has always been a problem. To be logged into two accounts at the same time.
Use multiple Gmail accounts at once
Life is now easier for people with multiple Gmail accounts. With the new multiple sign-in feature, you can toggle back and forth between accounts, or even have Gmail open in two tabs with different accounts. To learn more about this feature for advanced users, head over to the Gmail Blog.
Select each of the checkboxes below to confirm you understand how to use multiple sign-in:
Learn more about other ways to use multiple accounts with Google products.
