Chapter 5: Q 68. (page 309)

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

Short Answer

Expert verified

The obtained result is $\log [{(x^{3} + 1)}^{\frac{1}{3}} {(x^{2} + 1)}^{\frac{1}{2}}]$ .

Step by step solution

Step 1. Given Information.

Consider the given information.

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

Step 2. Calculation.

Apply the logarithm properties to combine the terms.

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

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

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Calculation.

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Write each expression as a single logarithm.13logx3+1+12logx2+1

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Calculation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

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Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

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