ln16

ln16 denotes the natural logarithm of the number 16. It is the power to which the base e must be raised to obtain 16, i.e., the value y such that e^y = 16. It is the natural logarithm with base e and can be written as ln(16) or log_e(16).

Since 16 = 2^4, the identity ln(16) = ln(2^4) = 4 ln(2) applies. Using ln(2) ≈ 0.6931471805599453, we obtain ln(16) ≈ 2.772588722239781. In common practice, this is often rounded to about 2.77 or 2.7726 depending on the desired precision.

Key properties: the natural logarithm is defined for positive inputs and is a strictly increasing function. Its derivative is 1/x, so d/dx ln(x) = 1/x for x > 0. It satisfies basic logarithm rules: ln(ab) = ln(a) + ln(b) and ln(a^k) = k ln(a). The value ln(1) equals 0, and e^{ln(16)} equals 16.

Applications: ln(16) appears in solving exponential equations where the unknown exponent is needed, such as determining x in e^x = 16. It is also used in calculus to evaluate integrals involving 1/x, in statistics and data analysis for log transformations, and in various scientific disciplines to linearize multiplicative relationships.