Can't achieve what I want in header / menu area

Hi

On my client’s site, I have set the header background color to be black.Unfortunately this also makes the background of the menu area black, which we don’t want. We’d like this background to be #f9f9f9. I couldn’t find a way to set this in theme options and have therefore added the following css:

#header_main_alternate {
background-color: #f9f9f9 !important;
}

All good, so far. Now, here’ what we’d like to achieve on one specific page only (URL in private content):

Make the background of the menu area transparent, but keep the background of the logo area black.

I’ve tried the follow css but the sides of the logo area is not black.

.page-id-5666 #header_main > .container {
background-color: #000 !important;
}

.page-id-5666 #header_main_alternate {
background: transparent !important;
}

What do I need to do to have the whole background in the logo area set to black please, like the rest of the site?

Thank you!