To rewrite \(\log(1100)\) using the Power Rule of Logarithms, which states that \(\log_b(k) = k \cdot \log_b(x)\), we should first break down \(1100\) into its prime factors:
\[ 1100 = 11 \times 100 = 11 \times 10^2 \]
Now we can express \(\log(1100)\) as follows:
\[ \log(1100) = \log(11 \times 10^2) \]
Using the logarithmic property that \(\log(a \times b) = \log(a) + \log(b)\):
\[ \log(1100) = \log(11) + \log(10^2) \]
Applying the Power Rule of Logarithms to \(\log(10^2)\):
\[ \log(10^2) = 2 \cdot \log(10) \]
So we can further express \(\log(1100)\):
\[ \log(1100) = \log(11) + 2 \cdot \log(10) \]
Without additional context about which logarithmic base is being used, we cannot directly match this into your provided options. However, from your options, it doesn't seem like any of them are quite right.
If we need to look for a specific manipulation to match one of the given answers, we can explore if any transformation can yield \(\log(1100)\) into a simpler form leading to one of the choices, such as scaling down logarithmic components. However, those options provided don't appear to directly correspond to a direct rewrite of \(\log(1100)\).
The closest option that would involve manipulating logarithms in a broader context doesn't seem to match without more specific instruction or context, so based on the breakdown above, we clearly find that none of the options accurately represent the log value of \(1100\).
If you need a conclusive answer from the provided options without a clear fit based on typical logarithmic transformations, then I'd say none match it correctly as shown above. But if you're asking for a simple re-expression of how one might move through logarithmic transformation, we can say:
\[ \log(1100) \neq \text{any option given directly.} \]
It's either \(log(11) + 2 \cdot \log(10)\) or another manipulation absent here.