Use the properties of logarithms to write the logarithm in terms of $\log _{3}(5)$ and $\log _{3}(7)$.
\[
\log _{3}\left(\frac{7}{25}\right)
\]

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Final Answer: $\boxed{\log _{3}(7) - 2\log _{3}(5)}$

Steps

Step 1 ：Given the expression $\log _{3}\left(\frac{7}{25}\right)$

Step 2 ：Using the properties of logarithms, specifically the quotient rule, we can rewrite the expression as $\log _{3}(7) - \log _{3}(25)$

Step 3 ：Next, we express 25 as $5^2$ and apply the power rule of logarithms to rewrite $\log _{3}(25)$ as $2\log _{3}(5)$

Step 4 ：Substituting this back into our expression, we get $\log _{3}(7) - 2\log _{3}(5)$

Step 5 ：Final Answer: $\boxed{\log _{3}(7) - 2\log _{3}(5)}$