If i keep any manual logs in the workflow i am able to see those logs in the workflow history but the default logs of the Assign task are not logging in the workflow history.
It is SharePoint designer workflow so you need to write log("any information"). Without writing this no log should be displayed. Whereas in ootb workflow you get log when task is assigned.
I am not sure what you want to see exactly.
But I the task related data will be saved in "Tasks" list associated with your workflow, not in workflow history list.