lnFxGx
lnFxGx is a notation used in mathematics to denote the natural logarithm of the product of two functions evaluated at a common argument x. The standard interpretation is ln(F(x) G(x)), the natural log of the product of F and G at x. Because of log rules, when F(x) and G(x) are positive, this quantity equals ln(F(x)) + ln(G(x)).
Notation can vary, and without parentheses the meaning may be ambiguous. Some authors might write ln F(x)
Domain and differentiation: If F and G are differentiable and positive on an interval, then ln(F(x) G(x))
Examples: If F(x) = e^x and G(x) = x^2 + 1 (which is positive for all real x), then
Applications: The expression commonly appears in probability, statistics (log-likelihoods for products of probabilities), information theory, and
See also: logarithm, natural logarithm, product rule, logarithm properties.