Right-click C:\Windows\System32\winevt\Logs in Windows Explorer.
Select Properties from the context menu.
If the Properties dialog has a Previous Versions tab, activate it.
If there is a previous version from after the shutdown, but before you cleared the log, you can open it or copy it to a different location (I wouldn't simply restore it, that probably isn't allowed).
Otherwise, you could try
Piriform Recuva to look for *.evtx files.
If Recuva hasn't been installed already on this PC, it's best to download the portable version on another computer and to copy it to a USB stick. Mount the USB stick on the problem computer and run Recuva from there. That way there is less chance of overwriting deleted files.
But don't hold your breath - the space of the deleted log files may already have been reused.