Question

Use a graphing utility to solve each equation. Express your answer rounded to two decimal places.

$e^{-x}=-\ln x$

Short answer

The solution of the given equation is 0.57.

Step-by-step solution

Step 1. Given information.

The given equation is:

$e^{-x}=-\ln x$

Step 2. Determine the solution by the graphing utility.

Plot the graphs of $y_1=e^{-x}$and $y_2=-\ln x$on a coordinate plane. The x-coordinate of the intersection point is the solution of the given equation.

The graphs intersect each other at $x\approx 0.567$. After rounding the value to two decimal places$x\approx 0.57$.

Step 3. Conclusion.

The solution of the given equation is 0.57.