Chapter 5: Q 69. (page 309)

Write each expression as a single logarithm.
$2 \log_{2} (x + 1) - \log_{2} (x + 3) - \log_{2} (x - 1)$

Short Answer

Expert verified

The result is $\log_{2} \frac{{(x + 1)}^{2}}{(x + 3) (x - 1)}$ .

Step by step solution

Step 1. Given information.

Consider the given information.

$2 \log_{2} (x + 1) - \log_{2} (x + 3) - \log_{2} (x - 1)$

Step 2. Calculation.

Write each expression as a single logarithm.

$\begin{array}{rcl} 2 \log_{2} (x + 1) - \log_{2} (x + 3) - \log_{2} (x - 1) & = & 2 \log_{2} (x + 1) - [\log_{2} (x + 3) + \log_{2} (x - 1)] \\ = & \log_{2} {(x + 1)}^{2} - [\log_{2} (x + 3) (x - 1)] \\ = & \log_{2} {(x + 1)}^{2} - \log_{2} (x + 3) (x - 1) \\ = & \log_{2} \frac{{(x + 1)}^{2}}{(x + 3) (x - 1)} \end{array}$

Step 3. Conclusion.

The obtained result is $\log_{2} \frac{{(x + 1)}^{2}}{(x + 3) (x - 1)}$ .

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.

Write each expression as a single logarithm.
$2 \log_{2} (x + 1) - \log_{2} (x + 3) - \log_{2} (x - 1)$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Calculation.

Step 3. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Pure Maths

Applied Mathematics

Statistics

Probability and Statistics

Decision Maths

Study anywhere. Anytime. Across all devices.

Write each expression as a single logarithm.2log2x+1-log2x+3-log2x-1

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Calculation.

Step 3. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Pure Maths

Applied Mathematics

Statistics

Probability and Statistics

Decision Maths

Study anywhere. Anytime. Across all devices.

Write each expression as a single logarithm.
$2 \log_{2} (x + 1) - \log_{2} (x + 3) - \log_{2} (x - 1)$