List files sorted numerically

Why not use the built-in ls feature for this particular case:

-v natural sort of (version) numbers within text

For example ls -1v log*

With GNU ls (i.e. on Linux, Cygwin, or other systems that have GNU ls specifically installed):

ls -v

In zsh:

echo *(n)

In other shells:

echo log?.gz log??.gz log???.gz

Replace echo by printf '%s\n' if you want each file name on a separate line.

If you want file metadata as well (ls -l) and you don't have GNU ls, you'll need to call ls separately for each file name or group of file names that you want to see in lexicographic order.

ls -ld log?.gz; ls -ld log??.gz; ls -ld log???.gz

To avoid these difficulties, use enough leading zeroes in your file names so that the lexicographic sort is human-friendly (log001.gz, etc).

bash's braces, {}, will enumerate them in order:

for file in log{1..164}.gz; do
    process "$file"
done