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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 70. (page 309)

Write each expression as a single logarithm.
$3 \log_{5} (3 x + 1) - 2 \log_{5} (2 x - 1) - \log_{5} x$

Short Answer

Expert verified

The result is $\log_{5} [\frac{{(3 x + 1)}^{3}}{{(2 x - 1)}^{2} x}]$ .

Step by step solution

01

Step 1. Given information.

Consider the given information.

$3 \log_{5} (3 x + 1) - 2 \log_{5} (2 x - 1) - \log_{5} x$

02

Step 2. Calculation.

Write each expression as a single logarithm.

$\begin{array}{rcl} 3 \log_{5} (3 x + 1) - 2 \log_{5} (2 x - 1) - \log_{5} x & = & \log_{5} {(3 x + 1)}^{3} - \log_{5} {(2 x - 1)}^{2} - \log_{5} x \\ = & \log_{5} {(3 x + 1)}^{3} - [\log_{5} {(2 x - 1)}^{2} + \log_{5} x] \\ = & \log_{5} {(3 x + 1)}^{3} - \log_{5} {(2 x - 1)}^{2} x \\ = & \log_{5} \frac{{(3 x + 1)}^{3}}{{(2 x - 1)}^{2} x} \end{array}$

03

Step 3. Conclusion.

The obtained result is $\log_{5} \frac{{(3 x + 1)}^{3}}{{(2 x - 1)}^{2} x}$ .

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Most popular questions from this chapter

In Problems 61鈥�72, the function f is one-to-one. Find its inverse and check your answer.

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