ln8

ln8 denotes the natural logarithm of the integer eight, written mathematically as ln(8). The natural logarithm uses the base e, where e is approximately 2.718281828459045. Because the exponentiated value e^x = 8 has the solution x = ln8, it quantifies the power to which e must be raised to produce eight. Conveniently, ln8 can be expressed exactly as three times the natural logarithm of two, since 8 equals 2 cubed: ln8 = ln(2^3) = 3·ln2. This relationship allows the use of known series or tables for ln2 to evaluate ln8.

Numerically, ln8 is about 2.079441541679835928. In base‑10 logarithms, it corresponds to log10(8) ≈ 0.903089987, because ln8 = log10(8)·ln10. The value appears in various mathematical contexts, such as computing integrals of the form ∫(1/x) dx, solving exponential growth models, and evaluating entropy in information theory where logarithms are taken with base e. In physics, ln8 sometimes arises in the solution of problems involving decay or multiplicative processes. Because ln8 is expressed simply in terms of ln2, it is often computed in scientific calculations by first determining ln2 and then multiplying by three.