I do not know of a direct way to automate a log to be printed. There might be a way to have a workflow rule run when a batch task completes and print the logs (but you would have to create a custom workflow and possibly develop a custom data model). You can manually see the logs from the TRA folder and print them or you can also see them via the log reading function (which you can also print from). You may want to contact your local business partner as there may be a customization or addon that does what you are looking for.

This may not be exactly what you are looking for, but could be a alternative solution.

You can setup a workflow where the triggering even type is "End of Task" and the event code being the task you are running (FUNAUTDLV). Setup the email recipient under the "Recipient" tab, and under the message tab, you can setup the email subject and body. Check the "Linked Trace File" checkbox to allow log file attachment.

By doing so, whenever FUNAUTDLV runs, it would email the log file to the the recipient. Please note that the task code here is referring to the X3 task code, NOT the recurring task code. If you want to only email the log when certain recurring task is triggered, you may want to add a condition under the general tab such as [F:ABR]CODABT = "your_recurring_task_code"