To understand why [tex]\(\log (387 \times 28)\)[/tex] is equal to [tex]\(\log 387 + \log 28\)[/tex], let's take a look at the properties of logarithms, specifically the property relating to the logarithm of a product.
One of the key properties of logarithms is the Product Property, which states:
[tex]\[
\log_b (xy) = \log_b x + \log_b y
\][/tex]
This property applies to any base [tex]\(b\)[/tex] and positive numbers [tex]\(x\)[/tex] and [tex]\(y\)[/tex]. It simplifies the computation of the logarithm of a product by breaking it down into the sum of the logarithms of the individual numbers.
In this case, we have [tex]\(\log (387 \times 28)\)[/tex]. According to the Product Property of logarithms, we can write this as:
[tex]\[
\log (387 \times 28) = \log 387 + \log 28
\][/tex]
Thus, the value of [tex]\(\log (387 \times 28)\)[/tex] is the same as the sum [tex]\(\log 387 + \log 28\)[/tex]. Therefore, the correct answer is:
C. The logarithm of a product of two numbers is equal to the sum of logarithms of the numbers.
