Problem
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. \[ 3 e^{x}=131 \] The solution set expressed in terms of logarithms is (Use a comma to separate answers as needed. Simplify your answer. Use integers or fractions for any numbers in the equation.) Now use a calculator to obtain a decimal approximation for the solution. The solution set is (Use a comma to separate answers as needed. Round to two decimal places as needed.)
Solution
Step 1 ：Divide both sides of the equation by 3 to isolate the exponential term: \(e^{x} = \frac{131}{3}\)
Step 2 ：Take the natural logarithm of both sides to solve for x: \(x = \ln\left(\frac{131}{3}\right)\)
Step 3 ：Use a calculator to obtain a decimal approximation for the solution: \(x \approx 3.78\)
Step 4 ：Final Answer: The solution set expressed in terms of logarithms is \(\ln\left(\frac{131}{3}\right)\). The decimal approximation for the solution is \(\boxed{3.78}\)
