To determine which expression is equivalent to [tex]\(\log 9w\)[/tex], we use the logarithmic property which states that the logarithm of a product is the sum of the logarithms of the factors.
The property is:
[tex]\[
\log(ab) = \log(a) + \log(b)
\][/tex]
In this case, we have [tex]\(\log(9w)\)[/tex]. Here, [tex]\(a = 9\)[/tex] and [tex]\(b = w\)[/tex].
Applying the property, we get:
[tex]\[
\log(9w) = \log(9) + \log(w)
\][/tex]
So, the correct equivalent expression to [tex]\(\log(9w)\)[/tex] is:
[tex]\[
\log 9 + \log w
\][/tex]
Hence, the correct answer is:
[tex]\[
\boxed{\log 9 + \log w}
\][/tex]
