$$ ln left( \frac { e ^ { 2 } } { 19 } \right) $$

Explanation:

Step1: Apply logarithm property

Use the property $\ln(\frac{a}{b})=\ln a-\ln b$. $$\ln\left(\frac{e^{2}}{19}\right)=\ln(e^{2})-\ln(19)$$

Step2: Use another logarithm property

Use the property $\ln(a^{b}) = b\ln a$. For $\ln(e^{2})$, since $\ln e = 1$, then $\ln(e^{2})=2\ln e$. $$\ln(e^{2})-\ln(19)=2\ln e-\ln(19)$$

Step3: Simplify

Since $\ln e = 1$, substitute it into the expression. $$2\ln e-\ln(19)=2\times1-\ln(19)=2 - \ln(19)$$

Answer:

$2-\ln(19)$