Very simple script to apply permissions to Windows Event Log.

ApplyWindowsEventLogPermissions.ps1

$username = "IIS APPPOOL\Identity"

Function Set-PermissionsForEventLogSecurity($username)
{
    $registryKeyPath = "HKLM:\SYSTEM\CurrentControlSet\Services\EventLog\Security"
    $acl = Get-Acl $registryKeyPath
    $inherit = [System.Security.AccessControl.InheritanceFlags]"ContainerInherit, ObjectInherit"
    $propagation = [System.Security.AccessControl.PropagationFlags]"None"
    $registryRights = [System.Security.AccessControl.RegistryRights]"QueryValue",
        [System.Security.AccessControl.RegistryRights]"EnumerateSubKeys",
        [System.Security.AccessControl.RegistryRights]"Notify",
        [System.Security.AccessControl.RegistryRights]"ReadPermissions"
    $registryAccessRule = New-Object System.Security.AccessControl.RegistryAccessRule($username, $registryRights, $inherit, $propagation, "Allow")
    $acl.AddAccessRule($registryAccessRule)
    $acl | Set-Acl -Path $registryKeyPath
}

Function Set-PermissionsForEventLog($username)
{
    $registryKeyPath = "HKLM:\SYSTEM\CurrentControlSet\Services\EventLog"
    $acl = Get-Acl $registryKeyPath
    $inherit = [System.Security.AccessControl.InheritanceFlags]"ContainerInherit, ObjectInherit"
    $propagation = [System.Security.AccessControl.PropagationFlags]"None"
    $registryRights = [System.Security.AccessControl.RegistryRights]"QueryValue",
        [System.Security.AccessControl.RegistryRights]"EnumerateSubKeys",
        [System.Security.AccessControl.RegistryRights]"Notify",
        [System.Security.AccessControl.RegistryRights]"ReadPermissions",
        [System.Security.AccessControl.RegistryRights]"SetValue",
        [System.Security.AccessControl.RegistryRights]"CreateSubKey"
    $registryAccessRule = New-Object System.Security.AccessControl.RegistryAccessRule($username, $registryRights, $inherit, $propagation, "Allow")
    $acl.AddAccessRule($registryAccessRule)
    $acl | Set-Acl -Path $registryKeyPath
}

Set-PermissionsForEventLog($username)
Set-PermissionsForEventLogSecurity($username)5