When you burn a log in your fireplace you are converting

When you burn a log in your fireplace you are converting cellulose into carbon dioxide and water.

Wood is made from cellulose. When wood burns, cellulose reacts with oxygen from the air and it forms carbon dioxide and water vapor. 

The reaction of the combustion of glucose is as follows:

C₆H₁₂O₆ + 6O₂ = 6 CO₂ + 6H₂O
When wood burns, we notice that it slowly disappears because it passes into the mentioned gases. The ash that is created is part of the wood that did not burn.