what is 3 ln 3 - ln 9 expressed as a single natural logarithm?\nln 3\nln 6\nln 18\nln 27

Explanation:

Step1: Use the power - rule of logarithms

The power - rule states that $n\ln a=\ln(a^{n})$. So, $3\ln3=\ln(3^{3})=\ln27$.

Step2: Use the quotient - rule of logarithms

The quotient - rule states that $\ln a-\ln b = \ln\frac{a}{b}$. We have $\ln27-\ln9$, and by the quotient - rule, $\ln27-\ln9=\ln\frac{27}{9}$.

Step3: Simplify the fraction

$\frac{27}{9} = 3$, so $\ln\frac{27}{9}=\ln3$.

Answer:

A. $\ln3$