By burning the wood log, its components get combined with oxygen. Therefore, if we weigh the wood log plus the weight of oxygen that was used to burn that particular log, we will find that the final weight is more than initial. This means that if we capture the products (CO2,H2O,C,CO,etc), we would have a greater mass than what we started with, as we have combined the log's components with oxygen in order to burn it. Hence mass cannot be destroyed by burning.