ozi403,
I'm not sure what you are looking for, but if you wanted to output your errors and your output to log files you could use something like this:
test_script.sh 2> test_script.errors 1> test_script.log
If you want to append to the files so that you have historical logs, touch the files first and then type:
test_script.sh 2>> test_script.errors 1>> test_script.log
Hope this helps.
John