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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. 28 (page 349)

Write each expression as a single logarithm: $\frac{1}{2} \ln (x^{2} + 1) - 4 \ln \frac{1}{2} - \frac{1}{2} [\ln (x - 4) + \ln x]$

Short Answer

Expert verified

Single logarithm for given expression is: $\ln [\frac{16 \sqrt{x^{2} + 1}}{\sqrt{x (x - 4)}}]$

Step by step solution

01

Step 1. Given information

A logarithmic expression: $\frac{1}{2} \ln (x^{2} + 1) - 4 \ln \frac{1}{2} - \frac{1}{2} [\ln (x - 4) + \ln x]$

02

Step 2. Required to find

Write the expression as a single logarithm.

03

Step 3. Simplification

$\frac{1}{2} \ln (x^{2} + 1) - 4 \ln \frac{1}{2} - \frac{1}{2} [\ln (x - 4) + \ln x]$

role="math" localid="1646388588093" $= \ln {(x^{2} + 1)}^{\frac{1}{2}} + \ln {(\frac{1}{2})}^{- 4} - \frac{1}{2} [\ln x (x - 4)]$

role="math" localid="1646388600233" $= \ln {(x^{2} + 1)}^{\frac{1}{2}} + \ln {(2)}^{4} + \ln {[x (x - 4)]}^{- \frac{1}{2}}$

role="math" localid="1646388794218" $= \ln \sqrt{x^{2} + 1} + \ln (16) + \ln [\frac{1}{\sqrt{x (x - 4)}}]$

$= \ln [\frac{16 \sqrt{x^{2} + 1}}{\sqrt{x (x - 4)}}]$

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Most popular questions from this chapter

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