How do I capture the output of a script if it is being ran by the task scheduler?

To supplement @user2744787's answer, here is a screenshot to show how to use cmd with arguments in a Scheduled Task:

Program/script: cmd

Add arguments: /c run_with_default_port.bat > IMQuantWebServices.log

The >> will append the log file, rather than overwriting it each time. The 2>&1 will also send errors to your log file.

cmd /c YourProgram.exe >> log.txt 2>&1

With stderr (where most of the errors go to):

cmd /c yourscript.cmd > logall.txt 2>&1

Try this as the command string in Task Scheduler:

cmd /c yourscript.cmd > logall.txt