Need a little more information
Which radio are you talking about? Marine VHF or SSB? Broadcast AM or FM?What brand is it? Have you noticed any other interference with other radio of TV signals? Does it show up as flashing in the TV picture?What kind of log? I am guessing you mean a knot-log.How did you turn off the log? Did that turn off anything else such as the depth sounder?Are you sure it was not the depth sounder or wind speed indicator causing this problem?Generally speaking, this may be a result of an electrical grounding problem (such as a ground loop) or it might be a signal coupling problem having to do with the way the wires are physically routed or shielded (or not). This might be an indication of a larger problem having to do with the grounding system on the boat. You will want to be careful not to permit (or else you should correct) inadvertant connections between the electrical and rf "grounds" and the boats bonding system.Practically speaking, you should check the wiring for breaks or bad or failing connections. Look carefully at crimped connections and wiggle them to see if the problem goes away or gets worse. Tighten up any screw terminals. Look for corrosion. You might be able to cure the problem by rerouting wires, shielding them, twisting them if they are not shielded, replacing them, or adding some filtering such as ferrite beads (also called toroids). You can put a clamp on toroid on most cables be they power or signal without much worry.A handheld AM transistor radio can be useful for detecting and physically isolating interference like this. Try tuning it around to see if it picks up the same interference.The term "ground loop" is a frequently misused term often tossed around by pony tailed guys on drugs as if they actually know something. It is often an issue in audio equipment and shows up on audio equipment as an unwanted hum. Your problem may not be properly called a ground loop but most of the same principles apply and then some. A boats grounding system has many more potential issues than a rock stars audio system. For more information than you ever wanted to know about ground loops - see the link