ln5

ln5 is the natural logarithm of the number five, meaning it is the logarithm base e of 5. It is the unique real number x such that e^x = 5. The value is approximately 1.6094379124341003. Because 5 = 10/2, ln 5 can also be written as ln 10 − ln 2, using common natural-log values.

As a function, the natural logarithm ln x is defined for x > 0, is strictly increasing, and satisfies the derivative d/dx (ln x) = 1/x. Its integral satisfies ∫ (1/x) dx = ln x + C, and the definite integral ∫_1^5 (1/t) dt equals ln 5. The natural logarithm is the inverse function of the exponential function, and thus ln 5 also represents the time parameter in growth or decay models with continuous compounding when a factor of 5 is reached.

In practice, ln 5 appears in various contexts, including change-of-base computations: log_b 5 = ln 5 / ln b. It is irrational, and under standard transcendence results (Lindemann–Weierstrass), ln 5 is transcendental, hence not expressible as a ratio of integers. This makes ln 5 a common constant in analytic calculations, approximations, and theoretical results involving exponential growth, entropy, and related areas.