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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 60. (page 309)

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

Short Answer

Expert verified

The obtained result is $\begin{array}{rcl} - 3 \log_{2} x \end{array}$ .

Step by step solution

01

Step 1. Given information.

Consider the given information.

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

02

Step 2. Calculation.

Apply the property $\log_{a} (M N) = \log_{a} M + \log_{a} N$ .

role="math" localid="1646760404139" $\begin{array}{rcl} \log_{2} (\frac{1}{x}) + \log_{2} (\frac{1}{x^{2}}) & = & \log_{2} (\frac{1}{x} 路 \frac{1}{x^{2}}) \\ = & \log_{2} (\frac{1}{x^{3}}) \\ = & \log_{2} 1 - \log x^{3} \\ = & - 3 \log_{2} x \end{array}$

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