Blue logs are created by using logs with a blue firelighter, a possible reward from any tier of clue scroll. When burned they create a blue fire, yielding 50 Firemakingexperience, which is 10 more than regular logs. Additionally, every attempt to make a blue fire is successful, unlike with regular fire.
Blue logs can be added to the Odd Old Man's pot-boiler, but the resulting fire will be normal and the logs will be lost.
Blue flames indicate a temperature much hotter than that of a normal fire. This increased heat is typically a product of burning hydrocarbons rather than organic material, meaning that for logs to burn blue, they would need to be coated in some form of fossil fuel. To accurately produce this result, the firelighter most likely would contain some form of oil.