Chapter 5: Q. 69 (page 284)

Solve the equation $3^{x^{3}} = 9^{x}$
and verify your results using a graphing utility.

Short Answer

Expert verified

Required solution set is ${0, \sqrt{2}, - \sqrt{2}}$

Step by step solution

Step 1. Given information

$3^{x^{3}} = 9^{x}$

Step 2. Calculations

$3^{x^{3}} = 9^{x} 3^{x^{3}} = 3^{2 x} i f a^{u} = a^{v} t h e n u = v x^{3} = 2 x x^{3} - 2 x = 0 x (x^{2} - 2) = 0 x (x - \sqrt{2}) (x + \sqrt{2}) = 0 x = 0, \sqrt{2}, - \sqrt{2}$

Step 3. Graphing solution

Graph $y = 3^{x^{3}}$ and $y = 9^{x}$ intersect at (0,1) , $(\sqrt{2}, 3^{2 \sqrt{2}}), (- \sqrt{2,}, 3^{- 2 \sqrt{2}})$

Hence the required solution set is ${0, \sqrt{2}, - \sqrt{2}}$ .

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 the equation $3^{x^{3}} = 9^{x}$
and verify your results using a graphing utility.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculations

Step 3. Graphing solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Decision Maths

Probability and Statistics

Statistics

Logic and Functions

Calculus

Study anywhere. Anytime. Across all devices.

Solve the equation3x3=9xand verify your results using a graphing utility.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculations

Step 3. Graphing solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Decision Maths

Probability and Statistics

Statistics

Logic and Functions

Calculus

Study anywhere. Anytime. Across all devices.

Solve the equation $3^{x^{3}} = 9^{x}$
and verify your results using a graphing utility.