GNU (Linux) uses the following:
tail -n 10 <logfile> | tac
tail -n 10 <logfile> prints out the last 10 lines of the log file and tac (cat spelled backwards) reverses the order.
BSD (OS X) of tail uses the -r option:
tail -r -n 10 <logfile>
For both cases, you can try the following:
if hash tac 2>/dev/null; then tail -n 10 <logfile> | tac; else tail -n 10 -r <logfile>; fi
NOTE: The GNU manual states that the BSD -r option “can only reverse files that are at most as large as its buffer, which is typically 32 KiB” and that tac is more reliable. If buffer size is a problem and you cannot use tac, you may want to consider using @ata’s answer which writes the functionality in bash.