Quantum corrections to the entropy of Einstein-Maxwell dilaton-axion black holes

We study the corrections to the entropy of Einstein-Maxwell dilaton-axion black holes beyond semiclassical approximations. We consider the entropy of the black hole as a state variable and derive these corrections using the exactness criteria of the first law of thermodynamics. We note that from this general frame-work the entropy corrections for "simpler" black holes like Schwarzschild, Reissner-Nordstr\"{o}m and anti-de Sitter-Schwarzschild black holes follow easily. This procedure gives us the modified area law as well.