the easiest way to do that would be to get the Weaver Xtreme “Plus” plugin which offesr two built in options to do that. The Site logo HTML in the Title / tagline options meant to do exactly what you want. Or eventually use the header widget Area with two widgets of different sizes, one for the logo and one for the Title Tagline.
The benefit of the header widget area is that you can define a different layout on phones where you may want the logo and the Title / tagline to stack instead of being besides each other.
Without the “Plus” plugin the best would probably be to hide the default Title; and tagline with the hide option found in Main options > Header > Title / Tagline section.
Then use a single widget in the header widget area, and insert the logo there floated left, with the title tagline using the title tagline shortcode (found in the Add-Ons page)
It would look something like
<img src=”LogoImageUrl” style=”float:left;”>[site_title matchtheme=true] [site_tagline matchtheme=true]