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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. 103 (page 1019)

In the following exercises, solve each equation.
$2^{x^{2} + 2 x} = \frac{1}{2}$

Short Answer

Expert verified

The answer is $x = - 1$

Step by step solution

01

Step 1. Given

The equation is $2^{x^{2} + 2 x} = \frac{1}{2}$

02

Step 2. Solve the equation

$2^{x^{2} + 2 x} = \frac{1}{2} 2^{x^{2} + 2 x} = 2^{- 1}$

Bases are same so the exponents should be equal.

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

03

Step 3. Check the answer

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

True

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Most popular questions from this chapter

In the following exercise, find the inverse of each function.

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