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The text from the image translates as follows:

**"Write the domain of the function \( f(x) = \log(5 - x) \) using appropriate interval notation. For example: \((0,1]\), \([0,1)\), or \((-\infty, \infty)\). You can copy the symbol \( \infty \) from here or use the symbol \(L\) instead."**

### Solution:

The function given is \( f(x) = \log(5 - x) \). To determine the domain of this function, we must ensure that the argument of the logarithmic function is strictly positive because the logarithm of a non-positive number is undefined in the real number system.

So, we need:
\[
5 - x > 0
\]
\[
x < 5
\]

Thus, the domain of the function is all values of \( x \) less than 5. In interval notation, the domain is:

\[
(-\infty, 5)
\]

### Final answer: 
The domain of the function is \( (-\infty, 5) \).

Would you like more details or have any questions?

Here are five related questions to expand this topic:
1. What would be the domain of the function \( f(x) = \log(x + 2) \)?
2. How does the domain change if the logarithm base changes, like in \( f(x) = \log_2(5 - x) \)?
3. What is the range of the function \( f(x) = \log(5 - x) \)?
4. How do you determine the domain of a logarithmic function that involves multiple variables, such as \( f(x) = \log(5 - x^2) \)?
5. Can you explain how the domain of logarithmic functions relates to the properties of exponential functions?

**Tip**: Always remember that the argument of a logarithmic function must be positive for real numbers. This principle helps in finding the domain efficiently!

Write the domain of the function f(x) = log(5 - x) using appropriate interval notation. For example: (0,1], [0,1), or (-∞,∞). You can copy the symbol ∞ from here or use the symbol L instead.

Learn how to determine the domain of the logarithmic function f(x) = log(5 - x). The solution covers the key concept of logarithmic function domains and how to express it using interval notation. Suitable for high school students in Grades 10-12.

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