Change log - user permissions to view
By default the Report Contact Logging Report (Summary), that is used to display the detailed logging, requires the permission CiviCRM: administer CiviCRM. 



You can change it to a permission that you feel comfortable with for your subset of users and save the report. Otherwise you need to create a new specific permission with an extension https://docs.civicrm.org/dev/en/latest/hooks/hook_civicrm_permission/.