How do I Create a Log File?

Question

Hi All
Been up for a while trying to figure this out with no luck.
I created an app that will uninstall a program and all of it's files.
example
try
                    do shell script "rm -rf /Applications/TestFakeApp"
          end try
          try
                    do shell script "rm -rf /Applications/TestFakeApp2"
          end try
          try
                    do shell script "rm -rf ~/Library/Preferences/com.FakeTestApp.plist"
          end try
          try
                    do shell script "rm -rf ~/Library/Preferences/com.FakeTestApp2.plist"
          end try
          try
                    do shell script "rm -rf ~/Library/Logs/FakeTestApp*"
          end try
          try
                    do shell script "rm -rf ~/Library/Application\\ Support/FakeTestApp"
          end try
there are alot more paths to remove but this is just a few for example
I want to be able to create a log.txt file on the desktop to show what has been removed and or what could not be removed.
I then tried by creating a text document by using
do shell script "touch ~/Desktop/test.txt"
tell application "Finder"
          open file ((path to desktop folder as text) & "test.txt") using ((path to applications folder as text) & "TextEdit.app")
end tell
but I don't know what to do next.
1. Have it check for each file to see if it was deleted or not
2. add it into the test.txt file
3. save the file once done
Any help would be appriciated.

Answer 1

Your version of it was simpler for me to understand..
Thank you
But having 1 issue with it.
I added some lines of non existing files to test if it did not delete them.
the log file showed they were deleted, but the files were never there to begin with.
I also added a return after each one write section so in the log file they would not be on the same line.
try
  do shell script "sudo -v" password "" with administrator privileges
end try
do shell script "touch ~/Desktop/my.txt"
delay 2
set myLog to open for access file ((path to desktop as text) & "my.txt") with write permission
set eof myLog to 0 -- reset the file contents... eliminate this line if you want to append to an existing log
delay 2
write "this is a test" & return to myLog
delay 1
write "Trying to delete Test
" to myLog
delay 1
try
  do shell script "rm -rf /Test" with administrator privileges
          write "Deleted Test
          " to myLog -- this will only execute if the above line doesn't trigger an error
on error
          write "Error deleting Test
          " to myLog
end try
delay 1
write "Trying to delete test2
" to myLog
try
  do shell script "rm -rf /test2" with administrator privileges
          write "Deleted Test2
          " to myLog -- this will only execute if the above line doesn't trigger an error
on error
          write "Error deleting test2
          " to myLog
end try
delay 1
write "Trying to delete test3
" to myLog
try
          do shell script "rm -rf /test3*
          " with administrator privileges
  write "Deleted Test2" to myLog -- this will only execute if the above line doesn't trigger an error
on error
          write "Error deleting test3
          " to myLog
end try
delay 1
write "Trying to delete test4
" to myLog
try
  do shell script "rm -rf /test4" with administrator privileges
          write "Deleted Test4
          " to myLog -- this will only execute if the above line doesn't trigger an error
on error
          write "Error deleting test4
          " to myLog
end try
close access myLog