Chapter 5: Q. 79 (page 284)

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

Short Answer

Expert verified

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

Step by step solution

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

Short Answer

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

One App. One Place for Learning.

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

Short Answer

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

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Logic and Functions

Probability and Statistics

Calculus

Decision Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.

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