lnfx
lnFx denotes the natural logarithm of a function F evaluated at x, written as ln(F(x)). It is a standard operation applied to a positive argument. The expression is defined precisely for all x for which F(x) > 0. If F is positive throughout its domain, ln(F(x)) is defined for all those x; otherwise ln(F(x)) is undefined where F(x) ≤ 0.
The derivative of ln(F(x)) with respect to x, when F(x) > 0 and F is differentiable, is F'(x)
Examples: If F(x) = x, then ln(F(x)) = ln x, defined for x > 0, with derivative 1/x. If
Applications: Taking the natural logarithm of a function is common when modeling multiplicative processes, converting products
Limitations: If F reaches zero or becomes negative, ln(F(x)) is undefined. In such cases, one may restrict