Question

Solve the exponential equation. Express the solution in terms of natural logarithms or common logarithms.​ Then, use a calculator to obtain a decimal approximation for the solution.
e Superscript x Baseline equals 13.26
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Part 1
The solution set expressed in terms of logarithms is StartSet nothing EndSet .
  
​(Use a comma to separate answers as needed. Simplify your answer. Use integers or decimals for any numbers in the expression. Use ln for natural logarithm and log for common​ logarithm.)

Answer 1

To solve the equation \( e^x = 13.26 \), we will take the natural logarithm of both sides.

1. Take the natural logarithm of both sides:
\[
\ln(e^x) = \ln(13.26)
\]

2. Using the property of logarithms that states \( \ln(e^x) = x \), we simplify the left side:
\[
x = \ln(13.26)
\]

So, the solution expressed in terms of logarithms is:
\[
\{ \ln(13.26) \}
\]

### Part 2: Decimal Approximation

Now, let's calculate the decimal approximation of \( \ln(13.26) \) using a calculator:

\[
\ln(13.26) \approx 2.89
\]

Therefore, the solution in terms of logarithms is \( \{ \ln(13.26) \} \) and the decimal approximation is approximately \( 2.89 \).