Problem
Maria Fleury 11/15/23 10:35 PM (?) Question 26, 3.4.51-Setup \& Solve HW Score: $62.7 \%, 26.33$ of 42 points Part 2 of 3 Points: 0.33 of 1 Save Solve the following logarithmic equation. Be sure to reject any value of $x$ that is not in the domain of the original logarithmic expression. Give the exact answer. Then, use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. \[ \ln x=5 \] Rewrite the given equation without logarithms. Do not solve for $\mathrm{x}$. \[ e^{5}=\mathrm{x} \] Solve the equation. What is the exact solution? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is $\{\square$. (Type an exact answer in terms of $e$.) B. There are infinitely many solutions. C. There is no solution.
Solution
Step 1 ：Rewrite the given equation without logarithms: \(e^{5} = x\).
Step 2 ：Solve the equation to find the exact solution: \(x = e^{5}\).
Step 3 ：Use a calculator to obtain a decimal approximation, correct to two decimal places: \(x = 148.41\).
Step 4 ：Final Answer: The exact solution to the equation is \(e^5\). The decimal approximation of the solution, correct to two decimal places, is \(\boxed{148.41}\).
