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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

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

01

Step 1. Given information.

Consider the given information.

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

02

Step 2. Calculation.

Write each expression as a single logarithm.

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

03

Step 3. Conclusion.

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

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Most popular questions from this chapter

Solve the equation ${(\frac{1}{4})}^{x} = \frac{1}{64}$

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