lnxy
lnxy commonly denotes the natural logarithm of the product of x and y, written as ln(xy). The natural logarithm is the logarithm with base e, where e is approximately 2.71828. The function is defined for real numbers when the product xy is positive, i.e., xy > 0. The standard identity is ln(xy) = ln x + ln y, which holds for x > 0 and y > 0. If either x or y is nonpositive, the real logarithm of xy is undefined; complex extensions exist but go beyond the real-valued setting.
This logarithmic rule enables the simplification of products inside logarithms and is a cornerstone of many
Examples help illustrate the rule: with x = 2 and y = 8, ln(xy) = ln(16) ≈ 2.772589, and ln