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I'm looking to attach three posts the the side of my house and I'm wondering if a ledger board is needed?

Looks like this:

Wood siding on a house is there for weather protection and looks, it has little structural strength. The ledger board is used to connect the patio cover beams to the internal structural members of the house walls for strength against wind shear forces and (possibly) snow loads that will want to pull your cover away from the house, spreading that force across as many internal structural members (studs) as possible. If you just attach the beams directly to the studs, you are attaching only to one stud and essentially concentrating the mechanical forces onto fewer points, increasing the stresses they will see. If they fail, it becomes major damage to your house walls.

If your connection points line up with the floor assembly for the floor above you can fasten to the rim joist.

If not you need someway to support half the weight of the structure at the house wall side. There are different approaches. Ledger is one. Posts for independent structure is another. If you have windows with headers that match the height of the connection point this can also work.

In the picture you've posted it is probable that there is a header over the sliding glass door. If they had this overhang in mind from the beginning they might have put blocking at the level required that spans between studs for the other connection points. Often studs will have fire blocking between them which tends to make them act as a structural system instead of just a single stud which is also tied to the top and bottom plates.