Which of the following is the correct expansion of log(xy)?

The expansion of log(xy) follows a fundamental property of logarithms known as the product rule. According to this rule, the logarithm of a product is equal to the sum of the logarithms of the individual factors. Therefore, when you have the expression log(xy), it can be rewritten as log(x) + log(y).

This property is a key concept in logarithmic functions and is widely used in simplifying logarithmic expressions and solving logarithmic equations. By understanding that log(xy) = log(x) + log(y), you can accurately expand the logarithm of a product into the sum of the logarithms of its components.

It's important to differentiate this from other potential options. For instance, the incorrect choice that suggests subtraction does not hold true under the properties of logarithms compared to the correct addition in this case. Similarly, the alternative choices that mention products or exponents do not align with the basic rules of logarithmic expansion, confirming that the correct response indeed represents the proper application of the logarithmic product rule.