https://file.aiquickdraw.com/mathbot/file/17274719128050fmhhtv9.jpg

The equation shown in the image is:

\[
e^{x - 3} = 20
\]

To solve for \( x \), follow these steps:

1. **Rewrite the equation** in logarithmic form. Taking the natural logarithm (ln) on both sides:
   \[
   \ln(e^{x - 3}) = \ln(20)
   \]
   
2. **Simplify** using the property of logarithms \( \ln(e^a) = a \):
   \[
   x - 3 = \ln(20)
   \]

3. **Solve for \( x \)** by isolating \( x \):
   \[
   x = \ln(20) + 3
   \]

4. **Calculate \( \ln(20) \)** using a calculator:
   \[
   \ln(20) \approx 2.9957
   \]
   
   So,
   \[
   x \approx 2.9957 + 3 = 5.9957
   \]

Thus, \( x \approx 5.9957 \) (rounded to four decimal places).

Let me know if you need further details!

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Here are 5 related questions to explore:

1. How do we apply logarithmic properties to solve exponential equations?
2. What is the relationship between natural logarithms and the base \( e \)?
3. How can you check if your solution to an exponential equation is correct?
4. What is the significance of the constant \( e \) in exponential functions?
5. How does rounding affect the precision of solutions in logarithmic calculations?

**Tip**: Always double-check your logarithmic values, especially when rounding to ensure accuracy in final solutions!

Solve the equation: e^(x - 3) = 20. (Round to four decimal places)

This page explains how to solve the exponential equation e^(x - 3) = 20. Learn how to use logarithmic properties, including taking the natural logarithm, to find the solution. The final answer is approximately x = 5.9957, rounded to four decimal places. This method is suitable for high school students in Grades 10-12.

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