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.

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