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e.g files:
-rw-r--r-- 1 root root 500000684 Jul 22 08:21 my_log.log.01_1500707421_500000684

ls -lrt *.log* | sed 's/^/echo "/; s/\([0-9]\{10\}\)/`date -d @\1`/; s/$/"/;'

echo "-rw-r--r-- 1 root root 500000684 Jul 22 08:21 my_log.log.01_`date -d @1500707421`_500000684"

s/\([0-9]\{10\}\)/`date -d @\1`/

\1 brings your reference from LHS to RHS

in this case; you could run eval for instance ..

eval $(ls -lrt *.log* | sed 's/^/echo "/; s/\([0-9]\{10\}\)/`date -d @\1`/; s/$/"/;') | sed 's/echo/\n/g'