Let's analyze the expression $\log(x - 4)$ to find its domain and range.

Domain:

The domain of a logarithmic function is determined by the argument of the logarithm. For the function $\log(x - 4)$, the argument is $x - 4$, and logarithms are only defined for positive values.

So, for the domain, we need: $x - 4 > 0$ Solving for $x$: $x > 4$ Thus, the domain of $\log(x - 4)$ is: $\boxed{(4, \infty)}$

Range:

The range of a logarithmic function is all real numbers. This is because the logarithmic function $\log(x)$ can produce any real number as an output as the argument varies within its domain.

Therefore, the range of $\log(x - 4)$ is: $\boxed{(-\infty, \infty)}$

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Would you like more details on logarithmic functions or further clarification on this problem?

Here are 5 related questions:

1. What happens to the domain and range if we have $\log(x + 4)$ instead?
2. How do the transformations of $\log(x)$ affect the domain and range?
3. What is the domain and range of $\log(2x - 5)$?
4. How can I graph $\log(x - 4)$?
5. What is the significance of the vertical asymptote in the graph of a logarithmic function?

Tip: Remember, the argument of the logarithm must always be positive for the function to be defined.