To find the vertical asymptotes for the function $y = \ln(x^2 - 4x)$, we need to determine where the argument of the logarithm, $x^2 - 4x$, is zero or undefined.

Step 1: Set the argument of the logarithm to zero

$x^2 - 4x = 0$

Step 2: Factor the equation

$x(x - 4) = 0$

Step 3: Solve for $x$

$x = 0 \quad \text{or} \quad x = 4$

Conclusion

The vertical asymptotes occur where the argument of the logarithm is zero because the logarithm function tends towards negative infinity at these points. Therefore, the vertical asymptotes for the function $y = \ln(x^2 - 4x)$ are:

$x = 0 \quad \text{and} \quad x = 4$

Would you like more detailed explanations or have any questions on this? Here are some related questions you might find interesting:

1. What happens to the function as $x$ approaches the vertical asymptotes?
2. How do we find horizontal asymptotes for functions?
3. Can logarithmic functions have horizontal asymptotes?
4. What is the domain of the function $y = \ln(x^2 - 4x)$?
5. How would you graph this function showing the asymptotes?

Tip: Always remember that logarithms are only defined for positive values. Ensure to find points where the argument inside the logarithm is greater than zero for the function to exist.