Solve the equation to four decimal places.
e Superscript xequals2.984
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Part 1
The solution is xalmost equals
  
enter your response here. ​(Round to four decimal​ places.)

To solve the equation \( e^x = 2.984 \), we need to isolate \( x \). 

1. Take the natural logarithm (ln) of both sides:

\[
\ln(e^x) = \ln(2.984)
\]

2. Simplify the left side using the property \( \ln(e^x) = x \):

\[
x = \ln(2.984)
\]

3. Calculate the natural logarithm of 2.984:

\[
x \approx \ln(2.984) \approx 1.0931
\]

So, the solution to the equation \( e^x = 2.984 \) is \( x \approx 1.0931 \) when rounded to four decimal places.

Would you like more details, or do you have any questions? 

Here are five related questions:
1. How would you solve \( e^x = 10 \) to four decimal places?
2. What is the general method for solving equations of the form \( e^x = a \)?
3. How can logarithmic properties help in solving exponential equations?
4. What is the relationship between natural logarithms and the exponential function?
5. How do you interpret the solution \( x = \ln(2.984) \) in practical terms?

**Tip:** When solving equations involving the exponential function, taking the natural logarithm is often the most straightforward approach to isolate the variable.

Learn how to solve the equation \( e^x = 2.984 \) to four decimal places with a detailed step-by-step solution. This problem covers key concepts in exponential functions and natural logarithms, providing insights into solving equations of this form.

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