Is it possible to have the console output echo / print to a text file, or log file?

( i.e. reading the info from memory, printing to a text file / log, instead of displaying on the console. )
OR
( i.e. reading the info from memory, printing to a text file / log, and displaying on the console. )

If possible, how?

Rough Analogy /

Linux example ( read and display on console ):
cat /proc/cpuinfo
Linux example ( read and save the output as a text file ):
cat /proc/cpuinfo >> cpuinfo.txt

The file /proc/cpuinfo is not a saved or stored text file. Kept in memory only.
Using a text editor on it causes problems, or finds nothing to see.
Reading it and piping the output to a text file works every time, with no problems.

/ Rough Analogy

Like Trudograd so far, keep up the good work. :)