Use a graphing utility to solve the equation.

The solution set is
(Use a comma to separate answers as needed. Round to
two decimal places as needed.)

Ask by Young Simmons. in the United States

Jan 20,2025

Question

Use a graphing utility to solve the equation. $$ e^{x}=-9 x $$ The solution set is $$ \{\square\} $$ (Use a comma to separate answers as needed. Round to two decimal places as needed.)

UpStudy AI · Accepted Answer

It seems that there is an issue with solving the equation $$e^{x}=-9x$$ using the provided method. Let's try to solve it manually.

To solve the equation $$e^{x}=-9x$$, we can use the natural logarithm to isolate $$x$$.

Taking the natural logarithm of both sides of the equation, we get:
$$ \ln(e^{x}) = \ln(-9x) $$

Using the property of logarithms that $$\ln(e^{x}) = x$$, we have:
$$ x = \ln(-9x) $$

Now, we can solve for $$x$$.

Let's solve the equation manually.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$x=\ln{\left(-9x\right)}$$
- step1: Find the domain:
  $$x=\ln{\left(-9x\right)},x<0$$
- step2: Move the expression to the left side:
  $$x-\ln{\left(-9x\right)}=0$$
- step3: Calculate:
  $$x\approx -0.100488$$
- step4: Check if the solution is in the defined range:
  $$x\approx -0.100488,x<0$$
- step5: Find the intersection:
  $$x\approx -0.100488$$
The solution to the equation $$e^{x}=-9x$$ is approximately $$x \approx -0.100488$$.

Therefore, the solution set is $$\{-0.100488\}$$.
The solution is approximately $$ x = -0.10 $$.

Use a graphing utility to solve the equation.

The solution set is
(Use a comma to separate answers as needed. Round to
two decimal places as needed.)

Upstudy AI Solution

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Use a graphing utility to solve the equation. The solution set is (Use a comma to separate answers as needed. Round to two decimal places as needed.)