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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 65. (page 309)

Write each expression as a single logarithm.
$8 \log_{2} \sqrt{3 x - 2} - \log_{2} (\frac{4}{x}) + \log_{2} 4$

Short Answer

Expert verified

The result is $\begin{array}{rcl} \log_{2} [x {(3 x - 2)}^{4}] \end{array}$ .

Step by step solution

01

Step 1. Given information.

Consider the given expression.

$8 \log_{2} \sqrt{3 x - 2} - \log_{2} (\frac{4}{x}) + \log_{2} 4$

02

Step 2. Calculation.

Apply the logarithm properties to combine the terms.

$\begin{array}{rcl} 8 \log_{2} \sqrt{3 x - 2} - \log_{2} (\frac{4}{x}) + \log_{2} 4 & = & 8 \log_{2} {(3 x - 2)}^{\frac{1}{2}} - \log_{2} 4 + \log_{2} x + \log_{2} 4 \\ = & \log_{2} {(3 x - 2)}^{\frac{8}{2}} + \log_{2} x \\ = & \log_{2} [x {(3 x - 2)}^{4}] \end{array}$

03

Step 3. Conclusion.

The obtained result is $\log_{2} \frac{{(3 x - 2)}^{4}}{x}$ .

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Most popular questions from this chapter

The function $f (x) = x^{4}$ is not one-to-one. Find a suitable restriction on the domain of $f$ so that the new function that results is one-to-one. Then find the inverse of $f$ .

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and verify your results using a graphing utility.

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