grep for special characters in Unix

Tell grep to treat your input as fixed string using -F option.

grep -F '*^%Q&$*&^@$&*!^@$*&^&^*&^&' application.log

Option -n is required to get the line number,

grep -Fn '*^%Q&$*&^@$&*!^@$*&^&^*&^&' application.log