In previous versions of PowerShell, session logging (transcripts) were supported only in the PowerShell console, and there could only be one transcript log active at a time.
In PowerShell 5.0, transcripts can be nested, and work in all hosts. Your script can easily start its own transcription in its own log file. Have a look:
PS> Start-Transcript Transcript started, output file is C:\Users\Tobias\Documents\PowerShell_transcript.DELL1.BGiNcMzC.20160330075046 .txt PS> Start-Transcript -Path C:\Temp\mylog.txt -Append Transcript started, output file is C:\Temp\mylog.txt PS> Stop-Transcript Transcript stopped, output file is C:\Temp\mylog.txt PS> Stop-Transcript Transcript stopped, output file is C:\Users\Tobias\Documents\PowerShell_transcript.DELL1.BGiNcMzC.20160330075046 .txt
As you can see, each call to Start-Transcript starts a new transcript session, and each call to Stop-Transcript stops the topmost session. When you use the -Path and –Append parameters, you can directly log input and output to your own log files. Just make sure your script stops any transcript that it started.