Finding log files that match number pattern

I have logs files which are generated each day depending on how many processes are running. Some days it could spin up 30 processes. Other days it could spin up 50. The log files all have the same pattern with the number being the different factor. e.g.

LOG_FILE_1.log
LOG_FILE_2.log etc etc

Is there a way to only return a subset of log files which match my criteria.. So say for example.... "Give me all the log files with numbers 3-20".. ignore all others ?

retrun in the sense you want to list it?
if yes..

 
ls -ltr LOG_FILE_[3-20].log

ls file[3-9].log file1[0-9].log file20.log

---------- Post updated at 19:26 ---------- Previous update was at 19:19 ----------

In a recent bash, you can set the option extglob , and then use

la log_file_*([3-9]|1[0-9]|20).log