Log e, also known as the natural logarithm, is the logarithm to the base e, where e is approximately 2.71828. On most calculators, it is represented by the 'ln' button, typically located near the standard log button. Users often recognize it as 'ln' rather than log e. The discussion emphasizes the importance of understanding this notation for mathematical calculations. Familiarity with the natural logarithm is essential for various applications in mathematics and science.