To determine which of the given expressions is equivalent to [tex]\(\log(22 \cdot 11)\)[/tex], we need to use the properties of logarithms.
One of the fundamental properties of logarithms is:
[tex]\[
\log(a \cdot b) = \log(a) + \log(b)
\][/tex]
This property states that the logarithm of a product is equal to the sum of the logarithms of the factors.
Let’s apply this property to the given problem:
[tex]\[
\log(22 \cdot 11) = \log(22) + \log(11)
\][/tex]
Thus, the expression [tex]\(\log(22 \cdot 11)\)[/tex] simplifies to:
[tex]\[
\log(22) + \log(11)
\][/tex]
Looking at the options provided:
A. [tex]\(\log(22) - \log(11)\)[/tex]
B. [tex]\(\log(22) \cdot \log(11)\)[/tex]
C. [tex]\(22 \cdot \log(11)\)[/tex]
D. [tex]\(\log(22) + \log(11)\)[/tex]
We can see that the correct expression, according to the logarithmic property we applied, is option D:
[tex]\[
\log(22) + \log(11)
\][/tex]
Therefore, the correct answer is:
D. [tex]\(\log(22) + \log(11)\)[/tex]
