I have a cron job:
$SP_s/StartDailyS1.sh >$LP_s/MirrorLogS1.txt
Where SP_s is the path to the script and LP_s
SP_s
LP_s
If you can do with having stdout/err in separate files, this should do:
($SP_s/StartDailyS1.sh 2>&1 >$LP_s/MirrorLogS1.txt.stdout) | tee $LP_s/MirrorLogS1.txt.stderr