Problem
Part 1 of 2 points Points: 0 of 1 Save 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.) example Get more help . Clear all Skill builder Check answer
Solution
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 \(\boxed{4.23}\)
