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

Step 1. Given information.

Consider the given information.

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

Step 2. Calculation.

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

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

Step 3. Conclusion.

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

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

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Calculation.

Step 3. Conclusion.

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Write each expression as a single logarithm.log4x2-1-5log4x+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

Statistics

Logic and Functions

Applied Mathematics

Geometry

Theoretical and Mathematical Physics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

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