ln102

ln102 refers to the natural logarithm of the positive number 102. In mathematics, the natural logarithm is the inverse function of the exponential function with base e, where e is approximately 2.71828. Therefore, ln(102) is the unique real number y such that e^y = 102.

Numerically, ln(102) ≈ 4.624973. This value is the natural log scale’s measure of how many factors of e are needed to reach 102 from 1. The natural logarithm has key properties: ln(ab) = ln(a) + ln(b) for positive a and b; ln(1) = 0; and its derivative with respect to x is 1/x, with the integral of 1/x giving ln(x) + C. It is concave on the positive real axis.

ln(102) often appears in contexts involving exponential growth or decay, continuous compounding, and entropy-related formulas in physics and information theory. It is related to other logarithms through change of base: ln(x) = log10(x) × ln(10) ≈ log10(x) × 2.302585.

In practice, ln(102) is typically evaluated with a calculator or computer software, and serves as a standard example of applying the natural logarithm to a concrete, non-round integer.