Q. 39 Solve each exponential equation.... [FREE SOLUTION]

91影视

Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 5: Q. 39 (page 315)

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

Short Answer

Expert verified

$x = \frac{1}{3} . \log_{2} \frac{8}{5} = \frac{1}{3} 鈰� \frac{\ln \frac{8}{5}}{3 \ln 2} 鈮� 0.226$

Step by step solution

Step 1. Given information

Solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. Verify your results using a graphing utility.

$5 (2^{3 x}) = 8$

Step 2. Explanation

$\begin{array}{l} {Wecansolveusingformulalog}_{a} a^{x} = x \\ Herea=2 \\ Soweget \\ 鈬� 2^{3 x} = \frac{8}{5} \\ 鈬� \log_{2} 2^{3 x} = \log_{2} \frac{8}{5} \\ 鈬� 3 x = \log_{2} \frac{8}{5} \\ 鈬� x = \frac{1}{3} . \log_{2} \frac{8}{5} \\ {Nowusingformulalog}_{a} M = \frac{\log_{a} M}{\log_{b} a} \\ Forbwewilltakeb=e \\ So, \\ x = \frac{1}{3} . \log_{2} \frac{8}{5} = \frac{1}{3} 鈰� \frac{\ln \frac{8}{5}}{3 \ln 2} 鈮� 0.226 \end{array}$

Step 3. Verify the result

Plot the graph of the given equation as shown below

Hence,

The solution to the equation is $x = 0.226$ .

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

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

Short Answer

Step by step solution

Step 1. Given information

Step 2. Explanation

Step 3. Verify the result

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Logic and Functions

Geometry

Probability and Statistics

Applied Mathematics

Decision Maths

Study anywhere. Anytime. Across all devices.

91影视

Solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. Verify your results using a graphing utility.5(23x)=8

Short Answer

Step by step solution

Step 1. Given information

Step 2. Explanation

Step 3. Verify the result

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Logic and Functions

Geometry

Probability and Statistics

Applied Mathematics

Decision Maths

Study anywhere. Anytime. Across all devices.

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