Try PowerShell 2.0's EventLog cmdlets. For PowerShell 2.0 and upwards:

• Run New-EventLog once to register the event source:

    New-EventLog -LogName Application -Source MyApp
  

• Then use Write-EventLog to write to the log:

    Write-EventLog 
        -LogName Application 
        -Source MyApp 
        -EntryType Error 
        -Message "Immunity to iocaine powder not detected, dying now" 
        -EventId 1
  

You can also use Windows PowerShell with the following command:

if ([System.Diagnostics.EventLog]::SourceExists($source) -eq $false) {
    [System.Diagnostics.EventLog]::CreateEventSource($source, "Application")
}

Make sure to check that the source does not exist before calling CreateEventSource, otherwise it will throw an exception.

For more info:

• http://msdn.microsoft.com/en-us/library/9t766zhb.aspx

eventcreate2 allows you to create custom logs, where eventcreate does not.

If someone is interested, it is also possible to create an event source manually by adding some registry values.

Save the following lines as a .reg file, then import it to registry by double clicking it:

Windows Registry Editor Version 5.00

[HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\services\eventlog\Application\YOUR_EVENT_SOURCE_NAME_GOES_HERE]
"EventMessageFile"="C:\\Windows\\Microsoft.NET\\Framework64\\v4.0.30319\\EventLogMessages.dll"
"TypesSupported"=dword:00000007

This creates an event source named YOUR_EVENT_SOURCE_NAME_GOES_HERE.

Or just use the command line command:

Eventcreate

However the cmd/batch version works you can run into an issue when you want to define an eventID which is higher then 1000. For event creation with an eventID of 1000+ i'll use powershell like this:

$evt=new-object System.Diagnostics.Eventlog(“Define Logbook”)
$evt.Source=”Define Source”
$evtNumber=Define Eventnumber
$evtDescription=”Define description”
$infoevent=[System.Diagnostics.EventLogEntryType]::Define error level
$evt.WriteEntry($evtDescription,$infoevent,$evtNumber) 

Sample:

$evt=new-object System.Diagnostics.Eventlog(“System”)
$evt.Source=”Tcpip”
$evtNumber=4227
$evtDescription=”This is a Test Event”
$infoevent=[System.Diagnostics.EventLogEntryType]::Warning
$evt.WriteEntry($evtDescription,$infoevent,$evtNumber)

PowerShell 7

This answer worked great in 5.x for me but not in 7.x. After some sleuthing, I got the following working:

Import-Module Microsoft.PowerShell.Management -UseWindowsPowerShell
New-EventLog -LogName Application -Source MyApp

I stumbled upon the module to import via this SO answer. Apparently, there's a set of modules you can import for Windows only cmdlet's depending upon your needs. I'm still trying to figure out how you would determine which module to import based upon your cmdlet.

Building off @roufamatic's powershell answer [https://stackoverflow.com/a/7154777/4582204]...

You can only call New-EventLog once or else you get

New-EventLog : The "MyApp" source is already registered on the "localhost" computer.
At line:1 char:1
+ New-EventLog -LogName Application -Source MyApp
+ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    + CategoryInfo          : InvalidOperation: (:) [New-EventLog], InvalidOperationException
    + FullyQualifiedErrorId : Microsoft.PowerShell.Commands.NewEventLogCommand

You might "naively" think that you could call Get-EventLog to detect if your log and source already exist. Alas, that will only tell you what events have been logged to Application MyApp; it errors on zero log events for the source, and also on source does not exist, with the same error code (bug?). Or, Get-EventLog tells you about the logs, but the source property of them is empty (bug?).

Checking whether a log source exists before creating it requires Get-WinEvent and checking whether your source is in the list of ProviderNames returned:

if (-not (Get-WinEvent -Listlog Application | where ProviderNames -contains MyApp)) {
    New-EventLog -LogName Application -Source MyApp
}

To round out this topic, if you want to remove your log source, the command is (no -LogName Application needed or allowed):

Remove-EventLog -Source MyApp

Of course removing a source that does not exist also results in an error, so you may still have to check first.