To rewrite \( \log(r^3 n^2) \) using the properties of logarithms, we can apply the product and power rules.
The logarithm of a product can be expressed as the sum of the logarithms:
\[ \log(a \cdot b) = \log(a) + \log(b) \]
And the power rule applies as follows:
\[ \log(a^b) = b \cdot \log(a) \]
Now, applying these rules to \( \log(r^3 n^2) \):
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Start with the expression: \[ \log(r^3 n^2) \]
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Use the product rule: \[ = \log(r^3) + \log(n^2) \]
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Apply the power rule: \[ = 3\log(r) + 2\log(n) \]
So, the final rewritten form of \( \log(r^3 n^2) \) is:
\[ 3\log(r) + 2\log(n) \]
Therefore, the correct response is:
3logr + 2logn