We provide a simple derivation of the corrections for Schwarzschild and Schwarzschild-Tangherlini black hole entropy without knowing the details of quantum gravity. We will follow the ideas of Bekenstein, Wheeler, and Jaynes, using summation techniques without calculus approximations, to directly find logarithmic corrections to the well-known entropy formula for black holes. Our approach is free from pathological behavior giving negative entropy for small values of black hole mass M. With the aid of the "universality" principle, we will argue that this purely classical approach could open a window for exploring properties of quantum gravity.