Tail a log file with today`s date

So i am trying to come up with a command to tail a log file with todays date. The log file gets updated everyday with the current date. As the number of lines for the log for any particular day can vary from 2 lines to 20, so i want to tail all the results of the log file from todays date. Just to add that the format of the the date in log file is MM/DD/YY (04/25/16) and there is not way i would be able to change this as this is a legacy system. Below are some of the commands i tried but its not working, any idea what im doing wrong and what might work.
Thank you.

tail Output.log | grep $date(%m-%d-%y) This command doesnt show any results

tail Output.log $(date +"%m-%d-%Y") This one shows output but shows last 10 lines of the file