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 \(\boxed{3.78}\)

From Solvely APP
Source: https://solvelyapp.com/problems/8145/

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