how to set recurring todo tasks with org mode in emacs?

First thing is to understand that behavior of a header block in org mode is dictated by properties.

I want to set repeating task to have the following functions

• when I change from TODO state to DONE state, a header block will log “state changes” with time stamp.

That is all the requirement I need for recurring tasks.

This can be done by setting the following

• set :REPEAT_TO_STATE: property under the header with org-set-property
• set either DEADLINE (org-deadline) or SCHEDULE (org-schedule) with recurring syntax ¹ , for example, adding .+1d/+3d to timestamp represent recurring every 1 day or 3 day. (it will be randomly assigned by org mode.).

first you must set header as followed

* TODO work on quiz 3
DEADLINE: <2022-03-03 Thu  .+1w>
:PROPERTIES:
:REPEAT_TO_STATE: TODO
:LAST_REPEAT: [2022-03-02 Wed 16:26]
:END:

Then when you change from TODO to DONE state, header will log “state change” in a :LOGBOOK: property, and DONE state will automatically change to TODO. (so you will not see DONE state appears.). Deadline is then reset to the next date and time.

* TODO work on quiz 3
DEADLINE: <2022-03-03 Thu .+1w>
:PROPERTIES:
:REPEAT_TO_STATE: TODO
:LAST_REPEAT: [2022-03-02 Wed 16:26]
:END:
:LOGBOOK:
- State "DONE"       from "TODO"       [2022-03-02 Wed 16:26]
:END: