Some variations provide a process for producing mixed alcohols, comprising: purifying a biogas feedstock to generate a renewable natural gas stream comprising methane; introducing the renewable natural gas stream into a methane-to-syngas unit operated at effective conditions to convert the methane to a first syngas stream containing at least H2, CO, and CO2; purifying the first syngas stream, including separating the CO2 from the first syngas stream, and optionally separating some of the H2 from the first syngas stream, thereby generating a clean syngas stream; introducing the clean syngas stream into a mixed-alcohol reactor operated at effective alcohol synthesis conditions with an alcohol-synthesis catalyst, thereby generating mixed alcohols; and purifying the mixed alcohols to generate a mixed-alcohol product. The mixed-alcohol product may be blended with a hydrocarbon fuel, such as gasoline, to produce a blended fuel. The blended fuel has significantly lower carbon intensity than the base hydrocarbon fuel.