To rewrite the expression \( \ln 7 + 3 \ln w - 2 \ln x \) using the properties of logarithms, we can apply the Product Rule, Quotient Rule, and Power Rule as follows:
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Power Rule: Rewrite \( 3 \ln w \) as \( \ln w^3 \) and \( -2 \ln x \) as \( \ln x^{-2} \).
\[ \ln 7 + \ln w^3 + \ln x^{-2} \]
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Product Rule: Combine \( \ln 7 \) and \( \ln w^3 \):
\[ \ln (7 w^3) \]
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Quotient Rule: Now include \( \ln x^{-2} \):
\[ \ln \left( \frac{7 w^3}{x^2} \right) \]
So, the final expression is:
\[ \ln \left( \frac{7 w^3}{x^2} \right) \]
Among the given options, this expression matches with:
ln(7w³/x²), which corresponds to "the natural log of open paren the fraction with numerator 7 w cubed and denominator x squared close paren."
Thus, the correct choice is:
ln(7w³/x²).