Help logging out of Media & Purchases

I have a separate apple id connected to my Subscriptions. It pays for my apple music. I just got my mac and it won't allow me to login with that apple id. It would only let me login with my personal apple id. Now I am unable to login with the apple id that is being used for my Subscriptions. I am logged on to the apple id used for my Apple Music on my phone but it won't allow me to login to it on my Mac. I also can't find a way to log out of Media & purchases on my Mac to try to login with the Apple ID used for my subscriptions. I hope this makes sense. Please help me!