|Short answer is you don't need to know. When linking your program with
-lbluetooth should be enough, if it's installed in the usual place. Depending on what your development environment is, you can use pkg-config to tell you what flags you need to use to find headers and libs e.g
k5054@localhost:~$ pkg-config --cflags bluez
k5054@localhost:~$ pkg-config --libs bluez
k5054@localhost:~$This tells us that we don't need any additional flags for compilation, and only need to add -lbluetooth when linking.
If you really want to know where the lib is, you can use
dpkg to tell you where it is
k5054@localhost:~$ dpkg -S libbluetooth | grep .so
k5054@localhost:~$ Note that debian/ubuntu uses the target architecture as part of the filename for libraries, so for a PI with a 32 bit Raspberry Pi OS, the path is
/usr/lib/arm-linux-gnueabihf/libbluetooth.so.3, and it would be different again for a PI with a 64-bit OS, or an i386, MIPS, etc.
Keep Calm and Carry On