Problem
Solve the following 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. \[ e^{1-5 x}=2881 \] The solution set expressed in terms of logarithms is $\left\{\frac{1-\ln 2881}{5}\right\}$. (Use a comma to separate answers as needed. Simplify your answer. Use integers or fractions for any numbers in the expression. Use In for natural logarithm and log for common logarithm.) 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 ：Given the exponential equation \(e^{1-5x} = 2881\).
Step 2 ：Take the natural logarithm on both sides of the equation to isolate 'x'. This gives us \(1-5x = \ln 2881\).
Step 3 ：Solve for 'x' to get \(x = \frac{1-\ln 2881}{5}\).
Step 4 ：Use a calculator to find the decimal approximation of the solution, which gives us \(x = -1.3931785470169058\).
Step 5 ：Round to two decimal places as needed, the solution set is \(\boxed{-1.39}\).
