Which logs?
There are three views for logs: Process Logs, Object Logs, and Audit Logs.
There is a permission for each of them that you can set in System tab > Security > User Roles. You'd probably have to create a user role for them and then give them access to one or more of the following that are all part of the System Manager group of permissions
Audit - Audit Logs
Audit - Business Object Logs
Audit - Process Logs
Dave Morris, 3Ci at Southern Company