Logarithm is often used in physics and mathematics. It serves as a prerequisite for “What is entropy? From a microscopic point of view” and the articles in the section “Loop Quantum Gravity (for laymen).” “Expectation and Standard deviation” serves as a prerequisite for “A short introduction to quantum mechanics XII: Heisenberg’s uncertainty principle.” “Exponential function vs polynomial function” will play an important role in understanding my research on black hole entropy, which is reviewed in our article “Approximation of the na?ve black hole degeneracy.”