How can I restrict
sudo access to a specific user in the
/var directory or its contents?
sudo allows regular users to run commands as root. Unless you provide an explicit list of very specific commands it is virtually impossible to prevent a user with
sudo access from doing anything they like (and subsequently covering their tracks) with content that doesn't leave the server.
Your question is usually triggered by people who don't really grasp what
sudo is doing.
So, the only way to achieve what you want using
sudo is to limit the configuration to specific commands that don't accept any parameters.
sudo gives users root access (to everything, or to a subset of commands or to everything with some commands excluded).
If you don't trust users not to modify logs, then don't give them
sudo access, because
sudo access is just root access unless you're exceptionally careful and provide only specific commands (usually scripts) which achieve single specific goals.