Here is an alternative way to simulate using awk:
awk 'f==10{f=0; nextfile; exit} /regex/{++f; print FILENAME":"$0}' *.log
Explanation:
f==10 : f - this is the flag we set, and check if it is equal to 10. You can configure it depending on the number of lines you want to match.
nextfile : Moves the processing of the next file.
exit :Coming out of awk.
/regex/ :You are searching for regexor pattern.
{++f;print FILENAME":"$0} : We increase the flag and print the file name and line.