To rewrite the expression \( \log\left(\frac{r^3}{n^2}\right) \) using the Quotient Rule of Logarithms, we can apply the following rules of logarithms:
- The Quotient Rule states that \( \log\left(\frac{a}{b}\right) = \log(a) - \log(b) \).
- The Power Rule states that \( \log(a^k) = k \cdot \log(a) \).
Now let's apply these rules step by step to rewrite \( \log\left(\frac{r^3}{n^2}\right) \):
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Apply the Quotient Rule: \[ \log\left(\frac{r^3}{n^2}\right) = \log(r^3) - \log(n^2) \]
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Now apply the Power Rule to both terms:
- For the first term: \[ \log(r^3) = 3 \cdot \log(r) \]
- For the second term: \[ \log(n^2) = 2 \cdot \log(n) \]
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Combine these results: \[ \log\left(\frac{r^3}{n^2}\right) = 3 \cdot \log(r) - 2 \cdot \log(n) \]
Therefore, the expression \( \log\left(\frac{r^3}{n^2}\right) \) can be rewritten as:
\[ 3 \cdot \log(r) - 2 \cdot \log(n) \]
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