To be able to enable the functionality that allows your users to edit their log entries, you need to have access to the General settings.
Note that only users with the Account admin role have access to these settings.
If you want to enable log entry editing, go to the General settings, and select "Log settings".
From here, you'll see the sections "Log settings", and "Log tools".
Click the switch on the right side of the section called "Enable log entry editig":
Click "Save log settings" to save the settings.
Note:
Enabling this functionality makes the option to edit log entries available to all users.
This also includes all old logs in your account.
If someone edits a log entry in the log feed, you'll see the version history of that log entry, so you'll still always see who has posted the log entry, what changes was made to the log entry, and when the log entry was posted. You'll also be able to see who has made changes to the entry.