By default the API logging is turned off. You can turn logging on by uncommenting the following line in the cxf.xml that is supplied in the default P6 Integration API server deployment:
<!-- <cxf:logging /> -->
After removing the comment markers, the line would appear as follows:
<cxf:logging />
Note: You can find the cfx.xml here: p6ws.war\WEB-INF\classes\cxf.xml