How do I use variables in single quoted strings?

Solution 1:

Variables are expanded in double quoted strings, but not in single quoted strings:

 $ name=World

 $ echo "Hello $name"
 Hello World

 $ echo 'Hello $name'
 Hello $name

If you can simply switch quotes, do so.

If you prefer sticking with single quotes to avoid the additional escaping, you can instead mix and match quotes in the same argument:

 $ echo 'single quoted. '"Double quoted. "'Single quoted again.'
 single quoted. Double quoted. Single quoted again.

 $ echo '"$name" has the value '"$name"
 "$name" has the value World

Applied to your case:

 echo 'test text "here_is_some_test_text_'"$counter"'" "output"' >> "$FILE"

Solution 2:

use printf:

printf 'test text "here_is_some_test_text_%s" "output"\n' "$counter" >> ${FILE}