Heard what sounded like water slowly dripping from stairwell outside the 2nd-floor bathroom when the bathtub is draining. Following sound location down to the 1st floor, discovered a black drainage pipe with soaked floor and stud but no water on the outside of the pipe. When I opened up the wall on the other side I found that the pipe was wet. Later when the shower was used in the 2nd upstairs bathroom, I checked the pipe and found it was wet on one side. I am thinking there is likely a leak at the joint where the line changes from vertical to horizontal since there is leaking whenever draining water from both bathrooms. Am I on the right track? If I am correct and find the joint leaking is reapplying the joint glue all I need to do or will I need a plumber?
Usually if it is a joint leak with PVC or ABS piping it is the best to cut out the failed parts and replace with new properly glued parts. The PVC or ABS parts are relatively inexpensive and can actually be a reasonable DIY project to replace.
The type of cement used to join PVC and ABS pipes to fittings is a solvent that softens the surfaces and then when they are slid together they weld as one. It is not at all effective to try to smear more of the solvent onto the outside of a joint. In addition to that PVC ans ABS materials have the characteristic that many other types of glues do not effectively adhere to it.
You may be able to do a temporary type of repair if you clean and dry the area very well and then apply some silicone sealer to the leak area. Silicone sealer will adhere to clean dry PVC/ABS but if it is wet then it will not. This is only temporary and a proper fix as outlined above should be done as soon as reasonably possible.
Simply applying solvent (i.e. "joint glue") to the outside of the joint will not result in a permanent fix. If the joint was improperly done the only fix is to disassemble the section and fix it. Generally this means cutting the bad parts out since you usually cannot pull badly assembled joints apart, and then putting new and correctly joined parts back.
If you're not comfortable with these procedures, you may be better off calling a plumber.