Gas logs come in 2 varieties:
1) Ventless gas logs are designed to be burned with the damper closed and are rated as ventless gas heaters. Because ventless gas logs are burned with the damper closed, all of the heat they produce will come into your room, so they are appropriate for those who need heat. The burner system of a ventless gas log is designed to burn the gas with complete combustion (or at least 99.9% complete combustion). The byproducts of burning natural gas or propane completely are water vapor and carbon dioxide, which are both harmless in moderation. Ventless gas logs will burn with a more nerveous and less natural looking flame that has more blue in it. In most cases, the burner is designed to produce flames in specific pattern so that it avoids actually touching the logs, making them less realistic in appearance. This is because when the flame hits the logs it gets cooler, which causes incomplete combustion of the gas...resulting in the production of Carbon Monoxide and Soot. Ventless gas logs also produce a smell that some equate to that of burning kerosene.They cannot be burned for extended periods of time because they tend to deplete the oxygen in your room as well as produce excessive amounts of moisture. Ventless gas logs are required to have a metal label permanently chained or attached to the burner system with operational instructions and warnings. If your gas log set has such a label, it will tell you that it is a ventless gas log.
2) Vented gas logs MUST be burned with the damper open. Although most of the heat goes up the chimney, their burner systems produce a much more realistic lofty yellow flame that looks very much like that of a real wood fire. The realistic looking flames are produced by allowing an air to fuel mixture that causes incomplete combustion to occur. As mentioned previously, the byproducts of burning incomplete combustion of natural gas (or LP) are Carbon Monoxide, Carbon Dioxide, Soot and Water Vapor, hence the reason that vented gas logs must be burned with the damper opened. You will also find that the flames of vented gas logs will come in direct contact with the logs and flow around them randomly (again, much like a real fire). Vented gas logs are not required to have the same labeling as ventless gas logs, but if there is a noticeable amount of soot on the logs, you can be pretty sure they need to be burned with the damper open. Whenever there is soot, there is Carbon Monoxide!
Vented gas logs also require that you "Never" close the damper while they are installed in the fireplace. They all come with some sort of clamp that is supposed to be attached to your damper so that the damper cannot accidentally be closed all the way. The damper clamp is there so that if you forget to open the damper, it will already be opened. It also will allow natural gas to escape up the chimney in the event there is a gas leak or someone turns on the logs without lighting them.