The only 100% reliable way to how to export .max files to some alternative 3D modeling format is to use the original 3ds Max (previously known as 3D Studio Max) software due to the proprietary and closed nature of the format.
Nevertheless, some dedicated conversion solutions like the PolyTrans|CAD+DCC also support formats from 3ds Max and thus might most likely help you with max to obj conversion as wel.
Open MAX file Open OBJ fileA 3D CAD translation software