Hi Ahmed,
Don't worry, all can be sorted, even without using a black magic.
In your case problem is with the logo image itself.
It contain too much empty space around white brand label. Please open logo image in graphic editor, and crop image, keep only white element with 5px space around. Then save changes and upload a new file again to Joomla, change logo. You will see a big difference in logo size. Yes, will be bigger, more visible.
Look at my screenshot (red line), and you will see about what I am talking about ;]

and your logo doesn't need 1200px of width (this is website, not a poster), 480px will be totally OK. Just resize after, cropping.