Q.25 Write each expression as the sum... [FREE SOLUTION]

91影视

Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 5: Q.25 (page 349)

Write each expression as the sum and/or difference of logarithms. Express powers as factors.
$\ln {(\frac{2 x + 3}{x^{2} - 3 x + 2})}^{2}, x > 2$

Short Answer

Expert verified

$\ln {(\frac{2 x + 3}{x^{2} - 3 x + 2})}^{2} = 2 \ln (2 x + 3) - 2 \ln (x - 2) - 2 \ln (x - 1)$

Step by step solution

Given data

The expression is : $\ln {(\frac{2 x + 3}{x^{2} - 3 x + 2})}^{2}, x > 2$

Concept used

Properties of logarithms:

$\log_{a} (M N) = \log_{a} M + \log_{a} N$
$\log_{a} (\frac{M}{N}) = \log_{a} M - \log_{a} N$
$\log_{a} M^{r} = r \log_{a} M$
$a^{x} = e^{x \ln a}$

Evaluate

$\ln {(\frac{2 x + 3}{x^{2} - 3 x + 2})}^{2} = 2 \ln (\frac{2 x + 3}{x^{2} - 3 x + 2})$ ; Using property of logarithms

$\ln {(\frac{2 x + 3}{x^{2} - 3 x + 2})}^{2} = 2 \{\ln (2 x + 3) - \ln (x^{2} - 3 x + 2)\}$ ; Using property of logarithms

role="math" localid="1646483367708" $\ln {(\frac{2 x + 3}{x^{2} - 3 x + 2})}^{2} = 2 \ln (2 x + 3) - 2 \ln (x^{2} - 3 x + 2)$ ; Using distributive law

$\ln {(\frac{2 x + 3}{x^{2} - 3 x + 2})}^{2} = 2 \ln (2 x + 3) - 2 \ln \{(x - 2) (x - 1)\}$ ; By factorization

$\ln {(\frac{2 x + 3}{x^{2} - 3 x + 2})}^{2} = 2 \ln (2 x + 3) - 2 \{\ln (x - 2) + \ln (x - 1)\}$ ; Using property of logarithms

role="math" localid="1646483563558" $\ln {(\frac{2 x + 3}{x^{2} - 3 x + 2})}^{2} = 2 \ln (2 x + 3) - 2 \ln (x - 2) - 2 \ln (x - 1)$ ; By distributive law

Conclusion

Thus, $\ln {(\frac{2 x + 3}{x^{2} - 3 x + 2})}^{2} = 2 \ln (2 x + 3) - 2 \ln (x - 2) - 2 \ln (x - 1)$

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91影视

Write each expression as the sum and/or difference of logarithms. Express powers as factors.
$\ln {(\frac{2 x + 3}{x^{2} - 3 x + 2})}^{2}, x > 2$

Short Answer

Step by step solution

Given data

Concept used

Evaluate

Conclusion

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91影视

Write each expression as the sum and/or difference of logarithms. Express powers as factors. ln2x+3x2-3x+22,x>2

Short Answer

Step by step solution

Given data

Concept used

Evaluate

Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Discrete Mathematics

Geometry

Decision Maths

Statistics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Write each expression as the sum and/or difference of logarithms. Express powers as factors.
$\ln {(\frac{2 x + 3}{x^{2} - 3 x + 2})}^{2}, x > 2$