Which property of logarithms states that logb(xy) can be separated into two terms?

The property of logarithms that allows logb(xy) to be separated into two terms is known as the Product Rule. This rule states that the logarithm of a product is equal to the sum of the logarithms of the individual factors. In mathematical terms, this can be expressed as:

logb(xy) = logb(x) + logb(y)

This property is particularly useful when simplifying logarithmic expressions or solving logarithmic equations, as it breaks down complex products into simpler additive components. By applying the Product Rule, it becomes easier to work with logarithms in both theoretical contexts and practical applications.

The other properties, such as the Quotient Rule and Power Rule, serve different purposes in logarithmic manipulation, and the Common Logarithm refers specifically to logarithms with base 10. Understanding these distinctions helps in leveraging the appropriate rules for various logarithmic situations.