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: $8 = 4^{x^{2}} \times 2^{5 x}$

Short Answer

Expert verified

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

Step by step solution

Step 1. Given information

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

Step 2. Required to find

Solve the given equation to find x.

Step 3. Solving the equation

Given, $8 = 4^{x^{2}} \times 2^{5 x}$

$\Rightarrow 2^{3} = 2^{2 x^{2}} \times 2^{5 x}$

$\Rightarrow 2^{3} = 2^{2 x^{2} + 5 x}$

$\Rightarrow 2 x^{2} + 5 x = 3$

$\Rightarrow 2 x^{2} + 5 x - 3 = 0$

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

$\Rightarrow x = \frac{- 5 \pm \sqrt{5^{2} - 4 (2) (- 3)}}{2 (2)}$

$\Rightarrow x = \frac{- 5 \pm \sqrt{25 + 24}}{4}$

$\Rightarrow x = \frac{- 5 \pm \sqrt{49}}{4}$

$\Rightarrow x = \frac{- 5 \pm 7}{4}$

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

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

$\Rightarrow x = - 3, x = \frac{1}{2}$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

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: $8 = 4^{x^{2}} \times 2^{5 x}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Required to find

Step 3. Solving the equation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Decision Maths

Calculus

Logic and Functions

Applied Mathematics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

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=4x2×25x

Short Answer

Step by step solution

Step 1. Given information

Step 2. Required to find

Step 3. Solving the equation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Decision Maths

Calculus

Logic and Functions

Applied Mathematics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

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: $8 = 4^{x^{2}} \times 2^{5 x}$