https://file.aiquickdraw.com/mathbot/file/1725451483089tnkwllqk.jpg

The equation provided in the image is:

\[
13e^{5x} = 13
\]

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

1. **Divide both sides by 13** to simplify the equation:
   \[
   e^{5x} = 1
   \]

2. **Take the natural logarithm (ln) of both sides** to eliminate the exponential function:
   \[
   \ln(e^{5x}) = \ln(1)
   \]

3. Using the property of logarithms, \(\ln(e^y) = y\), the equation simplifies to:
   \[
   5x = \ln(1)
   \]

4. We know that \(\ln(1) = 0\), so:
   \[
   5x = 0
   \]

5. **Solve for \( x \)**:
   \[
   x = 0
   \]

So, the value of \( x \) is \( 0 \).

Would you like further details or have any questions about this solution?

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Here are some related questions you might find interesting:

1. How does the natural logarithm simplify \( e^x \) expressions?
2. What are the key properties of logarithms?
3. What happens when \( \ln(0) \) is evaluated?
4. How would the solution change if the right-hand side of the equation were a different number?
5. How does the solution method change for \( e^{kx} = b \) where \( k \) and \( b \) are constants?

**Tip:** When solving equations involving exponential functions, logarithms are a powerful tool for isolating the variable.

Learn how to solve the exponential equation 13e^(5x) = 13 by using logarithms and simplifying steps. This problem is suitable for students in Grades 10-12 and covers key concepts in exponential functions and logarithms.

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