Q.27 Write each expression as a singl... [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.27 (page 349)

Write each expression as a single logarithm.
$\ln (\frac{x - 1}{x}) + \ln (\frac{x}{x + 1}) - \ln (x^{2} - 1)$

Short Answer

Expert verified

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

Step by step solution

Given data

The expression is : $\ln (\frac{x - 1}{x}) + \ln (\frac{x}{x + 1}) - \ln (x^{2} - 1)$

Concept used

The properties of logarithms:

$\log_{a} (M N) = \log_{a} M + \log_{a} N$
$\log_{a} (\frac{M}{N}) = \log_{a} M - \log_{a} N$
$\log_{a} M^{r} = r \log_{a} M$
$a^{x} = e^{x \ln a}$

Evaluate

$\ln (\frac{x - 1}{x}) + \ln (\frac{x}{x + 1}) - \ln (x^{2} - 1) = \ln [\frac{x - 1}{x} 路 \frac{x}{x + 1}] - \ln (x^{2} - 1)$ ; Using property of logarithms

role="math" localid="1646485237427" $\ln (\frac{x - 1}{x}) + \ln (\frac{x}{x + 1}) - \ln (x^{2} - 1) = \ln (\frac{x - 1}{x + 1}) - \ln (x^{2} - 1)$ ; Simplifying

role="math" localid="1646485345292" $\ln (\frac{x - 1}{x}) + \ln (\frac{x}{x + 1}) - \ln (x^{2} - 1) = \ln [\frac{(\frac{x - 1}{x + 1})}{(x^{2} - 1)}]$ ; Using property of logarithms

role="math" localid="1646485414066" $\ln (\frac{x - 1}{x}) + \ln (\frac{x}{x + 1}) - \ln (x^{2} - 1) = \ln [\frac{(\frac{x - 1}{x + 1})}{(x + 1) (x - 1)}]$ ; Using algebraic expression $(a^{2} - b^{2}) = (a - b) (a + b)$

$\ln (\frac{x - 1}{x}) + \ln (\frac{x}{x + 1}) - \ln (x^{2} - 1) = \ln [\frac{1}{{(x + 1)}^{2}}]$ ; Simplifying

role="math" localid="1646485500859" $\ln (\frac{x - 1}{x}) + \ln (\frac{x}{x + 1}) - \ln (x^{2} - 1) = \ln {(\frac{1}{x + 1})}^{2}$

Conclusion

Thus, $\ln (\frac{x - 1}{x}) + \ln (\frac{x}{x + 1}) - \ln (x^{2} - 1) = \ln {(\frac{1}{x + 1})}^{2}$

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.

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

Write each expression as a single logarithm.
$\ln (\frac{x - 1}{x}) + \ln (\frac{x}{x + 1}) - \ln (x^{2} - 1)$

Short Answer

Step by step solution

Given data

Concept used

Evaluate

Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Statistics

Discrete Mathematics

Applied Mathematics

Pure Maths

Geometry

Study anywhere. Anytime. Across all devices.

91影视

Write each expression as a single logarithm.lnx-1x+lnxx+1-lnx2-1

Short Answer

Step by step solution

Given data

Concept used

Evaluate

Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Statistics

Discrete Mathematics

Applied Mathematics

Pure Maths

Geometry

Study anywhere. Anytime. Across all devices.

Write each expression as a single logarithm.
$\ln (\frac{x - 1}{x}) + \ln (\frac{x}{x + 1}) - \ln (x^{2} - 1)$