Hi @Roger Roger ,
If you want that user to only view the audit log, you can create a role group and add view-only audit log permission. Then add the user as a member of the new role group.
If user need to manage the audit log, you need to add audit log permission to the group.
(Kindly note: You have to assign the permissions in Exchange Online. )
Here is detailed description for audit logs for your reference: Search the audit log in the Microsoft Purview compliance portal - Microsoft Purview (compliance) | Microsoft Learn
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