Use the logarithm property: \( \ln \left( \frac{a}{b} \right) = \ln a – \ln b \).

\[ \ln \left( \frac{5}{3} \right) = \ln 5 – \ln 3 \]

Given: \( x = \ln 3 \), \( y = \ln 5 \).

\[ \ln 5 – \ln 3 = y – x \]

Answer: \( y – x \)

Recognize factors of 45: \( 45 = 9 \times 5 = 3^2 \times 5 \).

Use logarithm properties: \( \ln (ab) = \ln a + \ln b \), \( \ln (a^b) = b \ln a \).

\[ \ln 45 = \ln (3^2 \times 5) = \ln (3^2) + \ln 5 \]

\[ \ln (3^2) = 2 \ln 3 \]

\[ \ln 45 = 2 \ln 3 + \ln 5 \]

Substitute: \( \ln 3 = x \), \( \ln 5 = y \).

\[ \ln 45 = 2x + y \]

Answer: \( 2x + y \)