To understand why the value of [tex]\(\log (350 \times 21)\)[/tex] is the same as that of [tex]\(\log 350 + \log 21\)[/tex], let's review some fundamental properties of logarithms. One of the key properties is the Product Property of Logarithms.
The Product Property of Logarithms states that:
[tex]\[
\log_b (xy) = \log_b x + \log_b y
\][/tex]
This property tells us that the logarithm of a product [tex]\(xy\)[/tex] is equal to the sum of the logarithms of [tex]\(x\)[/tex] and [tex]\(y\)[/tex].
Now let's apply this to our specific question:
Given the expression [tex]\(\log (350 \times 21)\)[/tex], using the Product Property of Logarithms, we can split it into:
[tex]\[
\log (350 \times 21) = \log 350 + \log 21
\][/tex]
From this property, we see that the expression [tex]\(\log (350 \times 21)\)[/tex] is equivalent to [tex]\(\log 350 + \log 21\)[/tex].
Thus, the correct answer is:
C. The logarithm of a product of two numbers is the equal to the sum of logarithms of the numbers.
