The equation in the image is:

$y = 2 \ln(x^2) - \ln(x^2)$

To simplify this expression, we can apply logarithmic properties. Specifically, the property:

$\ln(a^b) = b \ln(a)$

Thus, we can rewrite the terms as:

$y = 2 \cdot 2 \ln(x) - 2 \ln(x)$ $y = 4 \ln(x) - 2 \ln(x)$

Now, combine the terms:

$y = (4 - 2) \ln(x)$ $y = 2 \ln(x)$

So the simplified expression for $y$ is:

$y = 2 \ln(x)$

Would you like further details or clarification on this? Here are five related questions to expand on this:

1. How does the logarithmic property $\ln(a^b) = b \ln(a)$ work in general?
2. What are other properties of logarithms that help in simplifying expressions?
3. Can the function $y = 2 \ln(x)$ be differentiated or integrated?
4. How do you solve logarithmic equations like $\ln(x) = 5$?
5. What is the domain of the function $y = 2 \ln(x)$?

Tip: When working with logarithms, it's important to remember that the argument of a logarithm must always be positive.