Chapter 5: Q 62. (page 309)

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

Short Answer

Expert verified

The result is $\begin{array}{rcl} \log \frac{(x + 2)}{(x + 1)} \end{array}$ .

Step by step solution

Step 1. Given information.

Consider the given information.

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

Step 2. Calculation.

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

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

Step 2. Calculation.

The obtained result is $\begin{array}{rcl} \log \frac{(x + 2)}{(x + 1)} \end{array}$ .

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

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Calculation.

Step 2. Calculation.

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Write each expression as a single logarithm.logx2+3x+2-2logx+1

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Calculation.

Step 2. Calculation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

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Theoretical and Mathematical Physics

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Study anywhere. Anytime. Across all devices.

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