Book edition 6th

Author(s) Sullivan

Pages 1200 pages

ISBN 9780321795465

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Short Answer

Solve given equation and verify your result using graphing utility.
$e^{x^{2}} = e^{3 x} . \frac{1}{e^{2}}$

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

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information

The given equation is :

$e^{x^{2}} = e^{3 x} . \frac{1}{e^{2}}$

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

Step 2. Get a single expression with base e on both sides.

Using law of exponents , get a single expression with base e on right side .

$e^{3 x} . \frac{1}{e^{2}} = e^{3 x} . e^{- 2} = e^{3 x - 2}$

Step 3. Comparing the expressions having same bases and solving for x .

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

$x^{2} = 3 x - 2 x^{2} - 3 x + 2 = 0$

Factorise above expression.

$(x - 1) (x - 2) = 0 (x - 1) = 0, (x - 2) = 0 x = 1, x = 2$

Step 4. Verification using graphing utility

Graph

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

Determine the point of intersection.

The graph intersects at $x = 1, x = 2$

So the solution set is ${1, 2}$ .

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Precalculus Enhanced with Graphing Utilities

Answers without the blur.

Short Answer

Solve given equation and verify your result using graphing utility.
$e^{x^{2}} = e^{3 x} . \frac{1}{e^{2}}$

Step by Step Solution

Step 1. Given information

Step 2. Get a single expression with base e on both sides.

Step 3. Comparing the expressions having same bases and solving for x .

Step 4. Verification using graphing utility

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Precalculus Enhanced with Graphing Utilities

Answers without the blur.

Short Answer

Solve given equation and verify your result using graphing utility. ex2 = e3x. 1e2

Step by Step Solution

Step 1. Given information

Step 2. Get a single expression with base e on both sides.

Step 3. Comparing the expressions having same bases and solving for x .

Step 4. Verification using graphing utility

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Solve given equation and verify your result using graphing utility.
$e^{x^{2}} = e^{3 x} . \frac{1}{e^{2}}$