Question
Properties of Logarithms with Any Base Quick Check
4 of 54 of 5 Items
Question
Expand the logarithm log3(h9)
.(1 point)
Responses
log3(h−3)
logarithm subscript 3 baseline left parenthesis h minus 3 right parenthesis
(h−2)
left parenthesis h minus 2 right parenthesis
log3h−2
logarithm subscript 3 baseline h minus 2
log3h2
Answers
GPT-4o mini
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.
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.