How can I verify that an email sent to a customer with their invoice has been sent? Is there an email log?

Welcome to the Community, Beverly. 

You can use the Audit Log report to verify if an email or a transaction was sent to your customer. I'm here to here to guide you on how.

1. Sign in to your QuickBooks Online (QBO).
2. Go to the Gear icon, then click on Audit Log.
3. Filter the User, Date changed, and Events to narrow down the results.
4. Hit Apply.

From there, review the history of your invoices. You can see the events from the Event column. You can also select the View link in the History column to open the audit history.

For more tips while tracking your invoice entries in QBO, you can open this article: Create invoices in QuickBooks Online.

Once you're ready to enter the payments, use this link as your guide: Record invoice payments in QuickBooks Online.

If you have any other follow-up questions about your emailed transactions, let me know by adding a comment below. I'm more than happy to help. Keep safe!