Question
Expand the logarithm log3(h9)
.(1 point)
Responses
log3h2
Start Fraction logarithm subscript 3 baseline h over 2 End Fraction
log3h−2
logarithm subscript 3 baseline h minus 2
log3(h−3)
logarithm subscript 3 baseline left parenthesis h minus 3 right parenthesis
(h−2)
left parenthesis h minus 2 right parenthesis
.(1 point)
Responses
log3h2
Start Fraction logarithm subscript 3 baseline h over 2 End Fraction
log3h−2
logarithm subscript 3 baseline h minus 2
log3(h−3)
logarithm subscript 3 baseline left parenthesis h minus 3 right parenthesis
(h−2)
left parenthesis h minus 2 right parenthesis
Answers
GPT-4o mini
To expand the logarithm \(\log_3(h^9)\), we can use the logarithmic identity:
\[
\log_b(m^n) = n \cdot \log_b(m)
\]
Applying this identity to \(\log_3(h^9)\):
\[
\log_3(h^9) = 9 \cdot \log_3(h)
\]
So the expanded form of \(\log_3(h^9)\) is:
\[
9 \cdot \log_3(h)
\]
Since none of the response options you provided match this result, ensure to verify whether the options align with this expansion or provide additional context if needed.
\[
\log_b(m^n) = n \cdot \log_b(m)
\]
Applying this identity to \(\log_3(h^9)\):
\[
\log_3(h^9) = 9 \cdot \log_3(h)
\]
So the expanded form of \(\log_3(h^9)\) is:
\[
9 \cdot \log_3(h)
\]
Since none of the response options you provided match this result, ensure to verify whether the options align with this expansion or provide additional context if needed.