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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. 104 (page 1019)

In the following exercises, solve each equation.
$3^{x^{2} - 2 x} = \frac{1}{3}$

Short Answer

Expert verified

The answer is $x = 1$

Step by step solution

01

Step 1. Given

The equation is $3^{x^{2} - 2 x} = \frac{1}{3}$

02

Step 2. Solve the equation

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

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

$3^{x^{2} - 2 x} = \frac{1}{3} 3^{{(1)}^{2} - 2 (1)} = \frac{1}{3} 3^{1 - 2} = \frac{1}{3} 3^{- 1} = \frac{1}{3} \frac{1}{3} = \frac{1}{3}$

True

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