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Solve the given exponential equation. Express the solution set in terms of natural logarithms or common logarithms. Then use a calculator to obtain a decimal approximation for the solution.
\[
2 e^{x}=137
\]
The solution set expressed in terms of logarithms is $\{\square\}$.
(Use a comma to separate answers as needed. Simplify your answer. Use integers or fractions for any numbers in the equation.)
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Answer
Final Answer: The solution set expressed in terms of logarithms is \(\boxed{4.23}\)
Step 1 ：Given the exponential equation \(2e^{x} = 137\)
Step 2 ：First, divide both sides of the equation by 2 to isolate \(e^{x}\), giving us \(e^{x} = 68.5\)
Step 3 ：Then, take the natural logarithm of both sides to solve for x, which gives us \(x = \ln(68.5)\)
Step 4 ：Using a calculator, we find that \(x \approx 4.23\)
Step 5 ：Final Answer: The solution set expressed in terms of logarithms is \(\boxed{4.23}\)
