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You seem to indicate that these filenames are contained in another file? If that is the case, what is the pathname of that file?
Do these filenames really have that many leading spaces as part of their filenames?
Are you trying to zip all of these log files into a single archive, or are you trying to zip each log file into a separate archive?
What utility do you want to use to zip these log files? (Different UNIX and UNIX-like operating systems use different utilities such as
zip,
gzip,
pack,
compress, or something else depending on what operating system you're using, what version of that operating system you're using, and what you intend to do with the archives you create.)