Bathroom vents terminates to attic. The Inspector recommended that it terminates to the outside. What is the best way to do this. Should I just place the bathroom vent next to the roof vent opening.
Oops, didn't see the pic when I first answered. That's not a plumbing stack vent, that's a fan vent.
The most code-compliant way to do it would be to give this exhaust its own path to the outside, by cutting a hole in the roof, fitting a vent cap, and running the vent to the cap, attaching and sealing it. You may or may not need a squirrelcage cap (which helps draw air out of the vent), but it will need to be capped to shelter the vent flue from rain. You MAY be able to get away with simply feeding it to the nearest roof vent, depending on the size and design of these, but it won't meet minimum code in most jurisdictions.
Here's why: a vent fan evacuates warm and usually very humid air from your bathroom or kitchen (you're most often venting steam from a shower or from boiling pots/pans). Your attic is an enclosed "cold zone"; it has the same temperature as the outside, which in winter across the northern US will be below freezing. If you exhaust this warm air into the attic, the water will condense onto your rafters and freeze, then thaw, wetting the wood and causing weathering damage, mold and rot over time. Even if it comes out right next to a roof vent, if the air can mingle with attic air, condensation onto wood can still occur.
You could vent out the wall with one of these guys
(Louvered Exhaust Vent)
Or out the roof with one of these
(Roof vent cap)
Either way, your inspector is correct. Blowing warm moist air into the attic is probably not the best idea.
It's also not a good idea to vent out the wall too close to the soffit vents, as the exhaust will just be sucked back into the attic through the soffit.