Sorry been out playing instead of surfing.
Transducer would normally be on the bottom edge of the transom where it meets the hull. The log usually has a thing that looks like a paddle wheel and is usually about 1-1½ inches diameter made in plastic.
What make is it?
I have a NASA dual unit (log and depth) which I have to say is pretty hopeless. It has a through hull paddle wheel which I managed to mount on the transom/hull line. Not too bad upto about 15 Kn, then just about shows 20 ish Kn when i'm doing 30+.
And the echo sounder cannot be relied upon over 10Kn. Again the mountings were through hull and meant for yachts that only do 10Kn max.