What does the expression logbA + logbC equal?

The expression ( \log_b A + \log_b C ) can be simplified using the logarithmic property that states the sum of two logarithms with the same base equals the logarithm of the product of their arguments. This property is mathematically represented as:

[

\log_b A + \log_b C = \log_b (A \cdot C)

]

Thus, when you see ( \log_b A + \log_b C ), it perfectly aligns with the property which leads to ( \log_b (A \cdot C) ). This explains why the correct answer is ( \log_b (A \times C) ), confirming that you multiply the arguments of the logarithms when adding their logarithmic values.

Other choices involve addition, subtraction, or division of the arguments, which do not adhere to the logarithmic properties related to addition, making them incorrect outcomes for the operation specified in the question.