What is the domain of

f(x) = ln(x)

(0,∞)

[0,∞)

(-∞,∞)

(1,∞)
None of these

The function \( f(x) = \ln(x) \) is defined only when the argument of the logarithm is positive, meaning \( x > 0 \). The logarithmic function cannot accept negative values or zero because the logarithm of a non-positive number is undefined in the real number system.

Thus, the correct domain of \( f(x) = \ln(x) \) is \( (0, \infty) \).

Therefore, the answer is **(0, ∞)**.

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Would you like more details on logarithmic functions or have any other questions?

Here are five related questions for further exploration:
1. What is the range of \( f(x) = \ln(x) \)?
2. How would the domain change for \( f(x) = \ln(x - 2) \)?
3. What is the derivative of \( f(x) = \ln(x) \)?
4. How do you evaluate \( \ln(1) \) and \( \ln(e) \)?
5. Can the logarithmic function \( \ln(x) \) be extended to complex numbers?

**Tip:** The natural logarithm, \( \ln(x) \), grows very slowly as \( x \) increases.

What is the domain of f(x) = ln(x)? (0,∞), [0,∞), (-∞,∞), (1,∞), None of these.

Understand how to find the domain of the logarithmic function f(x) = ln(x). Learn why the domain is restricted to positive values of x (0,∞) and explore related concepts in calculus. Suitable for high school students in Grades 10-12.

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