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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 10: Q. 10.29 (page 1015)

Solve:
$\frac{e^{x^{2}}}{e^{x}} = e^{2}$

Short Answer

Expert verified

By solving $\frac{e^{x^{2}}}{e^{x}} = e^{2}$ , the value of $x$ is $- 1, 2$

Step by step solution

01

Step 1. Given

An expression $\frac{e^{x^{2}}}{e^{x}} = e^{2}$

To solve the expression.

02

Step 2. Use the property of exponent

By using the property of exponent, $\frac{a^{m}}{a^{n}} = a^{m - n}$

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

03

Step 3. Write a new equation by setting the exponents equal.

Since the bases are same, the exponents must be equal.

$x^{2} - x = 2 x^{2} - x - 2 = 0 x^{2} - 2 x + x - 2 = 0 x (x - 2) + 1 (x - 2) = 0 (x - 2) (x + 1) = 0$

$x = 2, - 1$

The value of $x$ is $- 1, 2$

04

Step 4. Check the solutions.

When $x = - 1$ ,

$\frac{e^{{(- 1)}^{2}}}{e^{(- 1)}} = e^{2} e^{1 + 1} = e^{2} e^{2} = e^{2}$

When $x = 2$ ,

$\frac{e^{{(2)}^{2}}}{e^{2}} = e^{2} e^{4 - 2} = e^{2} e^{2} = e^{2}$

Hence the solution has been checked.

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Most popular questions from this chapter

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