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Lpg is readily available in all areas , it is cheap, it has moderate ignition temperature , it doesn't leaves any residueand it has no smell.
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Log is very cheap.....it is in abundance....it is not much harmful
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Wood has traditionally been used as kitchen fuel and is still predominantly being used in rural areas. burning of wood creates many air pollutants which can result in respiratory problems. moreover, incomplete oxidation during  burning of wood creates carbon monoxide which is a poisonous gas. LPG is much better because it burns without giving smoke. it produces lesser amount of air pollutants. complete oxidation during burning of LPG does not lead to carbon monoxide  production.
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LPG is a better fuel than WOOD 
LPG has less calorific value and produces more heat than wood
no residue is left by lpg
wood leaves ash as residue 
lpg emits only less smoke
wood releases more smoke which contains carbon dioxide.

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