Solve for t.

e Superscript tetequals=438438

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Part 1

Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

A.

The solution is

tequals=enter your response here.

​(Type an integer or a decimal. Do not round until the final answer. Then round to four decimal places as needed. Use a comma to separate answers as​ needed.)

B.

The solution is not a real number.

We are given the equation:

\[
e^t = 438
\]

To solve for \( t \), we take the natural logarithm (ln) of both sides:

\[
\ln(e^t) = \ln(438)
\]

Since \( \ln(e^t) = t \), we have:

\[
t = \ln(438)
\]

Now, let's calculate \( \ln(438) \):

\[
t = \ln(438) \approx 6.0813
\]

So, the solution is:

\[
t \approx 6.0813
\]

Thus, the correct choice is:
**A. The solution is \( t = 6.0813 \)** (rounded to four decimal places).

Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:
1. How would you solve the equation if it were \( e^{2t} = 438 \)?
2. What happens if you take the logarithm of a negative number?
3. How can the natural logarithm be used to solve exponential growth problems?
4. What is the relationship between \( e \) and \( \ln \)?
5. What would the value of \( t \) be if the equation were \( e^t = 1000 \)?

**Tip:** The natural logarithm \( \ln(x) \) is the inverse function of the exponential function \( e^x \).

Solve for t. e^t = 438. Select the correct choice below and, if necessary, fill in the answer box to complete your choice: A) The solution is t = (enter your response). B) The solution is not a real number.

Learn how to solve the exponential equation e^t = 438 by taking the natural logarithm on both sides. This solution involves the inverse relationship between exponential functions and logarithms and provides a step-by-step calculation to find t ≈ 6.0813. Suitable for students in Grades 10-12.

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