Solve the equation to four decimal places.

e Superscript xexequals=2.9842.984

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Part 1

The solution is 

xalmost equals≈enter your response here. 

​(Round to four decimal​ places.)

It seems there might be a formatting issue with the equation. Based on the context, it looks like you want to solve the equation \( e^x = 2.984 \) and round the solution to four decimal places.

Let's solve it:

1. Start with the equation:

\[
e^x = 2.984
\]

2. Take the natural logarithm (ln) of both sides to solve for \( x \):

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

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

\[
x = \ln(2.984)
\]

4. Calculate the natural logarithm:

\[
x \approx \ln(2.984) \approx 1.0932
\]

So, the solution to the equation \( e^x = 2.984 \) is \( x \approx 1.0932 \) when rounded to four decimal places.

Would you like any further explanation or details on this? 

Here are five related questions:
1. How would you solve the equation \( e^x = 7.5 \)?
2. What is the significance of the natural logarithm in solving exponential equations?
3. How can you use the property \( \ln(ab) = \ln(a) + \ln(b) \) in solving logarithmic equations?
4. How does the graph of \( y = e^x \) behave, and what does it tell you about solutions to equations like this?
5. What are some practical applications of solving equations involving \( e^x \)?

**Tip:** Always remember to round your final answer only at the end to avoid rounding errors during intermediate steps.

Learn how to solve the equation e^x = 2.984 and round the solution to four decimal places with a detailed step-by-step solution. This problem covers exponential functions and the natural logarithm, providing insights into solving equations involving exponential growth. Suitable for students in Grades 10-12.

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