System generated tasks will appear in the tasks log app, however manually created tasks do not. They will appear in the assigned individual's task list. If you manually create a task and assign it to someone else in the workspace, you will see it appear under 'delegated tasks' from your personal task list which helps to check status to see if it is completed. Once it is completed it will no longer appear under 'delegated tasks' area but will always be viewable under the item it is attached. For example if it is attached to a seller lead.