Yeah, i agree...
This is what i'd say:
Private costs include the costs to firms in areas of production and the price that consumers pay for the product that they ultimatly purchase. However, it can be seen that the untimate social cost will inevitable higher because of the negative externality created by the logging. For example, the degradation of the environment will reduce integenerational equity and may create pollution, costs which are borne by the public and are not included in the priovate costs of firms in the logging of rainforests...etc