you may consider this answer as enhancement .. usually I am using
tail -F <fileName> | grep --line-buffered <pattern> -A 3 -B 5
-F is better in case of file rotate (-f will not work properly if file rotated)
-A and -B is useful to get lines just before and after the pattern occurrence .. these blocks will appeared between dashed line separators
But For me I prefer doing the following
tail -F <file> | less
this is very useful if you want to search inside streamed logs. I mean go back and forward and look deeply