To solve the equation \( e^{3x} = 17 \), follow these steps:

1. **Take the natural logarithm (ln) of both sides**:  
   \[
   \ln(e^{3x}) = \ln(17)
   \]

2. **Simplify the left side**:  
   Using the logarithmic identity \(\ln(e^a) = a\), we have:
   \[
   3x = \ln(17)
   \]

3. **Solve for \( x \)**:  
   Divide both sides by 3:
   \[
   x = \frac{\ln(17)}{3}
   \]

4. **Calculate the value**:  
   \[
   x \approx \frac{2.8332}{3} \approx 0.9444
   \]

So, the solution is approximately \( x \approx 0.9444 \).

Would you like more details or have any questions?

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Here are some related questions:

1. How do you solve exponential equations with different bases?
2. What is the natural logarithm, and why is it important?
3. How can you apply logarithms to solve real-world problems?
4. What are some properties of the natural exponential function \( e^x \)?
5. How do logarithms relate to exponential growth and decay?

**Tip:** Always check your solution by substituting it back into the original equation.

Learn how to solve the exponential equation e^(3x) = 17 with a detailed step-by-step solution. This problem involves exponential functions and natural logarithms, suitable for advanced high school students.

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