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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 61. (page 309)

Write each expression as a single logarithm.
$\log_{4} (x^{2} - 1) - 5 \log_{4} (x + 1)$

Short Answer

Expert verified

The result is $\begin{array}{rcl} \log_{4} \frac{(x - 1)}{{(x + 1)}^{4}} \end{array}$ .

Step by step solution

01

Step 1. Given information.

Consider the given information.

$\log_{4} (x^{2} - 1) - 5 \log_{4} (x + 1)$

02

Step 2. Calculation.

Use the property $\log_{a} (\frac{M}{N}) = \log_{a} M - \log_{a} N$ .

$\begin{array}{rcl} \log_{4} (x^{2} - 1) - 5 \log_{4} (x + 1) & = & \log_{4} (x^{2} - 1) - \log_{4} {(x + 1)}^{5} \\ = & \log_{4} \frac{(x^{2} - 1)}{{(x + 1)}^{5}} \\ = & \log_{4} \frac{(x + 1) (x - 1)}{{(x + 1)}^{5}} \\ = & \log_{4} \frac{(x - 1)}{{(x + 1)}^{4}} \end{array}$

03

Step 3. Conclusion.

The obtained result is $\begin{array}{rcl} \log_{4} \frac{(x - 1)}{{(x + 1)}^{4}} \end{array}$ .

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