The logarithms of rational numbers have irrationality exponent 2 [pdf]

Researchers have proven that the logarithm of a rational number is irrational, with a specific exponent of 2. The proof is detailed in a PDF document available online, which provides a rigorous mathematical explanation of the concept. The logarithm of a rational number, when raised to the power of 2, yields an irrational result, according to the research.