What you do is make an extremely large version of the image, then apply the max-width to it when you insert it, that way your banner simply moves responsively with the browser.
You should really also add a max-width to your page container, that way you aren't trying to cover massive monitors. Seriously... people don't need to expand a browser across an entire widescreen display these days.
A more dangerous way... is you float left and right portions and use a middle section as background, so the banner technically looks the same. You may want to ditch that via media query for mobiles though and just deliver an alternative logo banner.
I say dangerous... due to the sheer amount of browser versions being used, it would be difficult to do that accurately for every type, though you could easily cover 98% or more IMO. Anyone using decade old browsers... just too bad.