Are there any security concerns with logging that a user changed their password? I'm already logging whenever an admin changes a users password for audit purposes, but is there a reason to not have a log of when each user changed their own password?

Edit: Answers to questions below

What is your expected gain from this?

A Mainly forensic. The ability to see who (user_id of admin or self) changed the password in case the user claims they were hacked.

Who would have access to these logs?

System administrators and possibly a small support team.

About what kind of accounts are we talking about?

User accounts on an e-learning platform i.e. teachers and students.

Also, do you have password expiration rules?

No. I'm talking about storing when every change of password was done, not only the last change.