You can't delete your own log. You can report it (click on the little yellow ! triangle that appears in the lower right hand side of the reply box) and then (in the report) ask for it to be deleted.
If you are not happy with what you've written, you have 24 hours (one full day) to change the text. Use the Edit button to go back into your posts and amend them if you wish. After 24hours however, the edit button will disappear from each post.