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Use zgrep "DATE=" <log> | head -n 1 to find the start date. Use zgrep "DATE=" <log> | tail -n 1 to find the end date. If you would like you can write a bash function to make this easier:

get_dates()
{
    for f in atm.log.*.gz; do
        echo $f
        zgrep "DATE=" $f | head -n 1
        zgrep "DATE=" $f | tail -n 1
	echo ""
    done
}

(If zgrep is unavailable, use less <log> to look at a gzipped log file. Scroll down a decent amount to DATE= to find the start date. Use SHIFT+g to go to the end of the file. Scroll up to DATE= to find the end date.)

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