You can redirect the output of a Powershell script to a file. This is called transcribing, and is very useful if you have some Powershell scripts as scheduled tasks and wish to log its output.

$ErrorActionPreference="SilentlyContinue"
Stop-Transcript | out-null
$ErrorActionPreference = "Continue"
Start-Transcript -Path "C:\transcript.log" -Append
#
# My script code goes here...
#
Stop-Transcript