In what way are the investigations comprising Husserl's Logical Investigations logical? It could be that they are like criminal investigations, in which the investigations are not themselves criminal but merely investigations into criminal matters. Thus, Husserl could be investigating logic in the sense that the subject of the investigations is logic.
But they could also be like an efficient investigation, where "efficient" indicates the manner in which the investigations are carried out. Thus, Husserl could be investigating logic in the sense that he is carrying out his investigations in a logical manner.
If the first sense is true, then one wants to know if there is a prescribed manner for carrying out the investigation into logic. (Presumably, one would have to do it logically; but is that all?) If the second, then one wants to know what the subject of the investigation is.