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To find the domain of the function \( f(x) = \log(x - 16) \), we need to identify where the argument inside the logarithm is positive. 

For the logarithmic function \( \log(x - 16) \) to be defined, the expression inside the logarithm must be greater than 0:

\[
x - 16 > 0
\]

Solving this inequality:

\[
x > 16
\]

Thus, the domain of the function \( f(x) \) is all \( x \) values greater than 16. In interval notation, this is written as:

\[
(16, \infty)
\]

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

Here are some related questions to explore:

1. What is the domain of \( f(x) = \log(2x + 3) \)?
2. How does the base of the logarithm affect the domain of a function?
3. What happens to the graph of \( f(x) = \log(x - 16) \) as \( x \) approaches 16 from the right?
4. Can the logarithm function ever be negative?
5. How do you find the domain of a composition of functions involving logarithms?

**Tip:** Always remember that the argument of a logarithmic function must be strictly positive.

Find the domain of the function f(x) = log(x - 16). Write your answer using interval notation.

Understand how to find the domain of the logarithmic function f(x) = log(x - 16). This detailed explanation guides you through the necessary steps, including solving the inequality x - 16 > 0. Perfect for high school students in Grades 9-12.

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