OK be gentle with me this is my first time on this Forum. In Outlook I am told an email was sent and I have seen the hard copy but I cannot find it. It must be deleted (if it was sent at all). So where do I look first? Is there a log of all incoming emails somewhere? Help much appreciated.

First place to look is in your Junk Mail folder.
Next, try searching all mail items for a word that is unique to that message or for the sender's email address.

Good luck!

What's your account type? POP or IMAP?
You may find out your mail from sent folder