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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 38. (page 308)

Write each expression as a sum and/or difference of logarithms. Express powers as factors.
$\log_{3} \frac{x}{9}$

Short Answer

Expert verified

The result is $\log_{3} x + 2$ .

Step by step solution

01

Step 1. Given information.

Consider the given information.

$\log_{3} \frac{x}{9}$

02

Step 2. Calculation.

Apply the logarithm property to simplify.

$\begin{array}{l} \log_{3} \frac{x}{9} = \log_{3} x + \log_{3} 9 \\ = \log_{3} x + \log_{3} 3^{2} \\ = \log_{3} x + 2 \log_{3} 3 \\ = \log_{3} x + 2 \end{array}$

03

Step 3. Conclusion.

The obtained result is $\log_{3} x + 2$ .

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