Question
Rewrite as a difference of logarithms using the Quotient Rule of Logarithms. Do not evaluate the logarithm. \( \log _{6}\left(\frac{9}{x}\right) \) Submit Question
Ask by Macdonald Nguyen. in the United States
Mar 15,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\[
\log_{6}\left(\frac{9}{x}\right) = \log_{6}(9) - \log_{6}(x)
\]
Solution
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Bonus Knowledge
The expression \( \log_{6}\left(\frac{9}{x}\right) \) can be rewritten using the Quotient Rule of Logarithms, which states that the logarithm of a quotient is the difference of the logarithms. Therefore, it becomes: \[ \log_{6}(9) - \log_{6}(x) \] Now you've expressed the logarithm of a fraction as the difference of two logarithms without evaluating them!
