Chapter 5: Q 63. (page 309)

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

Short Answer

Expert verified

The result is $- 2 \ln (x - 1)$

Step by step solution

Step 1. Given information.

Consider the given information.

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

Step 2. Calculation.

Apply the logarithm property to combine the terms.

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

Step 3. Conclusion.

The obtained result is $- 2 \ln (x - 1)$ .

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

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.lnxx-1+lnx+1x-lnx2-1

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Calculation.

Step 3. Conclusion.

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Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

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Study anywhere. Anytime. Across all devices.

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