privacy – Is the display of email addresses in the log file of the application allowed under GDPR

I am working on an application that relies entirely on the interaction of the user. In the logs of my applications, I log each interaction and print the email address to uniquely identify which user did what interaction.

This application log will only be visible to anyone other than:

  • Me
  • The next owner of the application if I sell the project
  • An administrator that I could hire if the workload becomes too heavy

Here is an example of a log record:

2019-01-24 14: 27: 20.954 INFO 32256 — [whatever-info] s.p.s.t.d.m.s.SomeClassThatPrintsTheLog: User registration with email address.

Is this allowed in the RPGD or do I have to hide the email address printed in any way? Or use another solution?