Question
11) Use the quotient rule to expand logv9 (3/x)
A. 3logv9 x
B. logv9 3 + logv9 x
C. logv9 3/logv9 x
D. logv9 3 - logv9 x
A. 3logv9 x
B. logv9 3 + logv9 x
C. logv9 3/logv9 x
D. logv9 3 - logv9 x
Answers
GPT-4o mini
To expand \(\log_{v9} \left(\frac{3}{x}\right)\) using the quotient rule of logarithms, we use the property:
\[
\log_b \left(\frac{a}{c}\right) = \log_b a - \log_b c
\]
Applying this to \(\log_{v9} \left(\frac{3}{x}\right)\):
\[
\log_{v9} \left(\frac{3}{x}\right) = \log_{v9} 3 - \log_{v9} x
\]
Thus, the correct answer is:
**D. \(\log_{v9} 3 - \log_{v9} x\)**
\[
\log_b \left(\frac{a}{c}\right) = \log_b a - \log_b c
\]
Applying this to \(\log_{v9} \left(\frac{3}{x}\right)\):
\[
\log_{v9} \left(\frac{3}{x}\right) = \log_{v9} 3 - \log_{v9} x
\]
Thus, the correct answer is:
**D. \(\log_{v9} 3 - \log_{v9} x\)**