What does logb(A x C) simplify to?

The expression logb(A x C) simplifies to logbA + logbC based on the logarithmic property known as the product rule. This rule states that the logarithm of a product of two numbers is equal to the sum of the logarithms of the individual numbers.

For example, if you have two positive numbers A and C, taking the logarithm base b of their product (A x C) can be expressed as:

logb(A x C) = logbA + logbC.

This property is foundational in logarithmic functions and is widely used in simplifying logarithmic expressions in algebra and calculus.

The other choices do not apply in this case. The second choice suggests a subtraction or difference which is not related to the logarithmic operations for multiplication. The third choice implies division, which pertains to the quotient rule rather than the product rule. The fourth choice incorrectly suggests a multiplication of logarithms, which is not how logarithmic functions combine in this context.