Using the logarithmic property for division, we can simplify the expression $\ln \left( \frac{x}{y} \right)$ as follows:

$\ln \left( \frac{x}{y} \right) = \ln(x) - \ln(y)$

This is the result of applying the rule:

$\ln \left( \frac{a}{b} \right) = \ln(a) - \ln(b)$

So, the simplified form is:

$\ln(x) - \ln(y)$

Would you like further clarification on logarithmic properties?

Here are some related questions:

1. How does the logarithmic property for multiplication simplify $\ln(xy)$?
2. What is the logarithmic property for exponents (i.e., $\ln(x^a)$)?
3. How does the change of base formula work with logarithms?
4. Can the logarithmic property be applied to any base, or only the natural logarithm?
5. How can we simplify $\ln(x + y)$ using logarithmic properties?

Tip: Always break down complex logarithmic expressions using basic properties like multiplication, division, and exponent rules.