To expand the logarithm \(\log_3(h^9)\) using the properties of logarithms, we can use the power rule, which states that \(\log_b(a^n) = n \cdot \log_b(a)\).
Applying the power rule, we get:
\[ \log_3(h^9) = 9 \cdot \log_3(h) \]
So, the expanded form is \(9 \cdot \log_3(h)\).
However, it looks like none of the responses given match this correctly. If you are looking at options, ensure you are considering the correct expansion according to the properties of logarithms. Based on typical logarithm properties, it's important to double-check if there might be further context or specific instructions related to your question or if there are more choices.