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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 5: Q. 41 (page 349)

Solve each equation. Express irrational solutions in exact form and as a decimal rounded to 3 decimal places. Verify your results using a graphing utility: $8 = 4^{x^{2}} 脳 2^{5 x}$

Short Answer

Expert verified

The solution set of $x = \{- 3, \frac{1}{2}\}$

Step by step solution

01

Step 1. Given information

An equation, $8 = 4^{x^{2}} 脳 2^{5 x}$

02

Step 2. Required to find

Solve the given equation to find x.

03

Step 3. Solving the equation

Given, $8 = 4^{x^{2}} 脳 2^{5 x}$

$鈬� 2^{3} = 2^{2 x^{2}} 脳 2^{5 x}$

$鈬� 2^{3} = 2^{2 x^{2} + 5 x}$

$鈬� 2 x^{2} + 5 x = 3$

$鈬� 2 x^{2} + 5 x - 3 = 0$

For quadratic equation, role="math" localid="1646577006317" $a x^{2} + b x + c = 0$ , using quadratic formula, $x = \frac{- b 卤 \sqrt{b^{2} - 4 a c}}{2 a}$

$鈬� x = \frac{- 5 卤 \sqrt{5^{2} - 4 (2) (- 3)}}{2 (2)}$

$鈬� x = \frac{- 5 卤 \sqrt{25 + 24}}{4}$

$鈬� x = \frac{- 5 卤 \sqrt{49}}{4}$

$鈬� x = \frac{- 5 卤 7}{4}$

$鈬� x = \frac{- 5 - 7}{4}, x = \frac{- 5 + 7}{4}$

$鈬� x = \frac{- 12}{4}, x = \frac{2}{4}$

$鈬� x = - 3, x = \frac{1}{2}$

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Most popular questions from this chapter

In Problems 61鈥�72, the function f is one-to-one. Find its inverse and check your answer.

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