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The problem involves finding the limit:

\[
\lim_{x \to 3} \frac{f(x) - f(3)}{x - 3}
\]

Given that \( f(x) = \ln(x) \), this expression can be identified as the definition of the derivative of \( f(x) \) at \( x = 3 \).

### Steps:
1. **Definition of derivative:**

   The derivative of a function \( f(x) \) at a point \( a \) is given by:

   \[
   f'(a) = \lim_{x \to a} \frac{f(x) - f(a)}{x - a}
   \]

   Here, \( f(x) = \ln(x) \) and \( a = 3 \). So the given limit represents \( f'(3) \).

2. **Derivative of \( f(x) = \ln(x) \):**

   We know that the derivative of \( \ln(x) \) is:

   \[
   f'(x) = \frac{1}{x}
   \]

3. **Evaluating at \( x = 3 \):**

   \[
   f'(3) = \frac{1}{3}
   \]

Thus, the limit is:

\[
\lim_{x \to 3} \frac{\ln(x) - \ln(3)}{x - 3} = \frac{1}{3}
\]

### Final answer:
\[
\boxed{\frac{1}{3}}
\]

Would you like further details or have any questions about this problem? 

Here are 5 related questions for further exploration:
1. How would you compute the derivative of \( \ln(x) \) using first principles?
2. What is the geometric interpretation of this limit?
3. How does this problem change if \( f(x) \) were a different logarithmic function?
4. Can you apply L'Hôpital's Rule to solve this limit?
5. How would you calculate the derivative of \( \ln(x) \) at any arbitrary point \( a \)?

**Tip:** When faced with a limit resembling the difference quotient, always check if it represents the derivative of a function at a specific point.

If f(x) = ln(x), then lim x→3 (f(x) - f(3)) / (x - 3)

Solve the limit problem using the definition of the derivative for the function f(x) = ln(x) at x = 3. This problem demonstrates core calculus concepts such as logarithmic functions and derivatives, ideal for high school or early college students.

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