Solve the equation to four decimal places.
e^x=5.841

Part 1
what is X

To solve the equation \( e^x = 5.841 \), we need to take the natural logarithm (ln) of both sides to isolate \( x \). Here's the solution step-by-step:

1. Start with the equation:
   \[
   e^x = 5.841
   \]

2. Apply the natural logarithm (ln) to both sides:
   \[
   \ln(e^x) = \ln(5.841)
   \]

3. Use the logarithmic property \( \ln(e^x) = x \):
   \[
   x = \ln(5.841)
   \]

4. Now, calculate \( \ln(5.841) \):
   \[
   x \approx 1.7642
   \]

So, the value of \( x \) is approximately \( 1.7642 \).

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

Here are 5 related questions you could explore:
1. What is the general method for solving exponential equations?
2. How can you solve \( e^{2x} = 8 \)?
3. What is the relationship between natural logarithms and exponential functions?
4. How do you calculate logarithms using a calculator?
5. What are some real-life applications of exponential growth?

**Tip:** Always use natural logarithms (ln) when dealing with base \( e \), the natural exponential function.

Solve the equation to four decimal places. e^x = 5.841. What is x?

Learn how to solve the exponential equation e^x = 5.841 by using natural logarithms (ln) to find x. This solution provides a step-by-step explanation, including logarithmic properties and calculations. Suitable for high school students in Grades 10-12.

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