Final answer:
The PowerShell operational log that shows which scripts have been run on the host is the 'Microsoft-Windows-PowerShell/Operational' log in the Windows Event Log, accessible via the Get-WinEvent cmdlet.
Step-by-step explanation:
In PowerShell, the operational log that indicates which scripts have been run on the host can be found in the Windows Event Log, under the 'Microsoft-Windows-PowerShell/Operational' log. To view these entries, you can use the Get-EventLog cmdlet or the Get-WinEvent cmdlet, specifying the log name. For example, Get-WinEvent -LogName 'Microsoft-Windows-PowerShell/Operational' will display events from this log, where you can find information about script executions, including start and end times, the identity of the user who ran the script, and the path to the script file.