To find the domain of the function $f(x) = \log(x + 5) - 4$, we need to determine where the logarithmic part, $\log(x + 5)$, is defined. The logarithmic function is only defined for positive arguments, so we need:

$x + 5 > 0$

Solving this inequality:

$x > -5$

Thus, the domain of $f(x)$ is all values of $x$ that are greater than $-5$.

In interval notation, the domain of $f$ is:

$(-5, \infty)$

Would you like further details on this solution, or do you have any questions?

Here are some related questions for further practice:

1. What is the range of $f(x) = \log(x + 5) - 4$?
2. How would you find the domain of a function involving a square root instead of a logarithm?
3. What transformations are applied to the basic logarithmic function to get $f(x) = \log(x + 5) - 4$?
4. How does the addition of 5 inside the logarithm affect the graph of the function?
5. What would happen to the domain if the function were $f(x) = \log(-x + 5) - 4$?

Tip: For logarithmic functions, always check the argument inside the logarithm to ensure it is positive.