You need to use WildCards (or Globbing Patterns) in the
grep command like this :
tail -f log | grep "some_string.*some_string"
.* (Also pointed by @dsstorefile1 in the comments) is the globbing pattern used here. To get more details on Globbing Patterns refer to manpages.
man 7 glob
Which will show this :
. (dot) : will match any single character (except end of line) ,
equivalent to ? (question mark) in standard wildcard expressions.
* (asterisk) : the proceeding item is to be matched zero or more times.
ie. n* will match n, nn, nnnn, nnnnnnn
but not na or any other character.
Now, Combining both of these you get :
.* (dot and asterisk) : match any string, equivalent to * in standard wildcards.
Also, as pointed by @Bob in comments, using
.*? is much better than