Chapter 5: Q. 78 (page 284)

Solve given equation and verify your result using graphing utility.
$e^{3 x} = e^{2 - x}$

Short Answer

Expert verified

The solution set is ${\frac{1}{2}}$ and it is verified through graph.

Step by step solution

Step 1. Given information

The given equation is :

$e^{3 x} = e^{2 - x}$

We have to solve for x and verify using graphing utility.

Step 2. Comparing the expressions having same bases and solving for x .

Since bases are same , therefore the exponential powers should also be the same.

$3 x = 2 - x 3 x + x = 2 4 x = 2 x = \frac{2}{4} x = \frac{1}{2}$

Step 3. Verification using graphing utility

Graph

$Y_{1} = e^{3 x} Y_{2} = e^{2 - x}$

Determine the point of intersection.

The graph intersects at $x = \frac{1}{2}$ .

So the solution set is ${\frac{1}{2}}$ .

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Solve given equation and verify your result using graphing utility.
$e^{3 x} = e^{2 - x}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Comparing the expressions having same bases and solving for x .

Step 3. Verification using graphing utility

One App. One Place for Learning.

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Solve given equation and verify your result using graphing utility.e3x=e2-x

Short Answer

Step by step solution

Step 1. Given information

Step 2. Comparing the expressions having same bases and solving for x .

Step 3. Verification using graphing utility

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Logic and Functions

Calculus

Applied Mathematics

Pure Maths

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Solve given equation and verify your result using graphing utility.
$e^{3 x} = e^{2 - x}$