To solve the equation $e^x = 5.398$, we need to isolate $x$. This involves taking the natural logarithm of both sides. Here are the steps:

1. Start with the equation: $e^x = 5.398$

2. Take the natural logarithm (ln) of both sides: $\ln(e^x) = \ln(5.398)$

3. Use the property of logarithms that $\ln(e^x) = x \cdot \ln(e)$ and $\ln(e) = 1$: $x = \ln(5.398)$

Now, we just need to calculate the natural logarithm of 5.398 to four decimal places.

$x \approx \ln(5.398)$The solution to the equation $e^x = 5.398$ is $x \approx 1.6860$ when rounded to four decimal places.

Would you like more details or have any questions? Here are 8 related questions to expand on this information:

1. What is the base $e$ in natural logarithms?
2. How can you verify the solution by substitution?
3. What is the importance of the natural logarithm in mathematics?
4. How does changing the value of $5.398$ affect the solution?
5. What are some real-world applications of exponential equations?
6. How would you solve the equation $e^{2x} = 5.398$?
7. What is the difference between natural logarithms and common logarithms?
8. How can you use logarithms to solve equations involving other bases?

Tip: Remember that natural logarithms are useful for solving equations involving exponential growth or decay.