Yes, precisely. exp() is the mapping from so(3) to SO(3), so you can use log to go the other way around.
Here is the relationship with the other representations [1]
Where it becomes interesting for our rigid-body transform application (or recovery of it, in the case of computer vision), is with Twist coordinates (6 element vector) which will map to a 4x4 Transform, again using the matrix exp() operator [2].