Look at remote event log

This script will look in the Security EventLog at machinename
for EventId 680 and display the last 5.

$logs=[System.Diagnostics.EventLog]::GetEventlogs("machinename")
$app = $logs |? {$_.log -eq 'security'}
$myError = $app.entries | ? {$_.eventid -eq '680'}
$myError | Select-Object -Last 5

To look at the whole security log you can do like this:

$logs=[System.Diagnostics.EventLog]::GetEventlogs("machinename")
$app = $logs |? {$_.log -eq 'security'}
$app.entries

Last 10 events from the security log

$logs=[System.Diagnostics.EventLog]::GetEventlogs("machinename")
$app = $logs |? {$_.log -eq 'security'}
$app.entries | Select-Object –Last 10