This section defines the natural logarithm function exclusively within its rigorous mathematical framework as the inverse operation of the exponential growth curve with a base equal to Euler's number ($e$). The concept establishes $y = \ln(x)$ as the unique real-valued function satisfying $\exp(\ln(x)) = x$, characterized by an asymptotic behavior at zero and unbounded extension toward infinity. It serves as a foundational transcendental function in calculus, providing the necessary domain definition for analyzing continuous growth rates and solving differential equations involving natural bases without numerical approximation error.
Explains Euler's number e and the natural logarithm: e from continuous compounding, ln(x) as the inverse of e^x, and the key identities used when manipulating logs.