Chapter 5.6, Problem 63AYU

In Problems 69-82, use a graphing utility to solve each equation. Express your answer rounded to two decimal places.

$e^x=-x$

To determine

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

$e^x=-x$

Answer to Problem 63AYU

$x\approx -0.57$

Explanation of Solution

Given:

$e^x=-x$

Calculation:

1. Take the natural logarithm of both sides of the equation to remove the variables from the exponent.

2. Use logarithm rules to move $x$ out of the exponent.

3. Use the natural logarithm of $e$ is 1. That is, $in\left(e\right)=1$.

4. Graph each side of the equation. The solution is the $x$-value of the point of intersection.

Given equation is $e^x=-x$.

$\text{In}(e^x)=\text{ In}\left(-x\right)$

$x\text{In}\left(e\right)=\text{ In}\left(-x\right)$

$x.1=\text{ In}\left(-x\right)$   (since $\text{In}\left(e\right)=1$)

$x=\text{ In}\left(-x\right)$

By the above graph we get the value of $x$.

$x\approx -0.567143$

$x\approx -0.57$