What does logbA + logb(A x C) equal?

The expression you provided, logbA + logb(A x C), can be simplified using properties of logarithms. The property that applies here is the logarithm of a product. Specifically, the logarithmic identity states that the sum of the logarithms can be expressed as the logarithm of the product:

logbA + logb(A x C) = logb(A) + logb(A) + logb(C).

To break this down: logb(A x C) can be rewritten using the properties of logarithms as logbA + logbC, meaning that you are essentially adding the logarithm of C to logbA, which would combine to give you:

logb(A) + (logb(A) + logb(C)) = logb(A) + logb(A) + logb(C).

In essence, logb(A x C) alone encompasses both A and C, making it correct to say:

logbA + logb(A x C) simplifies directly to logb(A x C).

This understanding confirms that logbA + logb(A x C) indeed equals logb(A x C), which is why the stated choice is valid.