Phex has a simle query log already build in.
To activate it close Phex

Locate the phex.cfg file in the phex subfolder of your home directory.

Locate the entry:
searchMonitorFile=

Adjust it to something like:
searchMonitorFile=c:\\temp\\query.log

Start Phex and activate the search monitor in the user interface.

Phex now log search terms to c:\temp\query.log

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