Find the solution of the exponential equation $11 e^{x}-12=8$ The exact solution, in terms of the natural logarithm is: $x=.59$ The approximate solution, rounded to 4 decimal places is: $x=$
Answer
\(\boxed{x=0.598}\) is the exact solution and \(\boxed{x=0.5978}\) is the approximate solution.
Step 1 ：The given equation is \(11 e^{x}-12=8\).
Step 2 ：To solve for \(x\), we first need to isolate the exponential term \(e^{x}\) on one side of the equation.
Step 3 ：Then, we can take the natural logarithm of both sides to solve for \(x\).
Step 4 ：After that, we can calculate the approximate solution by rounding the exact solution to 4 decimal places.
Step 5 ：The exact solution of the equation in terms of the natural logarithm is \(x=0.598\).
Step 6 ：The approximate solution, rounded to 4 decimal places, is \(x=0.5978\).
Step 7 ：\(\boxed{x=0.598}\) is the exact solution and \(\boxed{x=0.5978}\) is the approximate solution.
