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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 46. (page 308)

Write each expression as a sum and/or difference of logarithms. Express powers as factors.
$\log_{2} (\frac{a}{b^{2}})$

Short Answer

Expert verified

The result is $\log_{2} a + 2 \log_{2} b$ .

Step by step solution

01

Step 1. Given information.

Consider the given information.

$\log_{2} (\frac{a}{b^{2}})$

02

Step 2. Formula used.

The logarithm properties are defined as,

$\begin{array}{l} \log_{a} (\frac{M}{N}) = \log_{a} M - \log_{a} N \\ \log_{a} M^{r} = r \log_{a} M \end{array}$

03

Step 2. Calculation.

Apply the logarithm property to simplify.

$\begin{array}{rcl} \log_{2} (\frac{a}{b^{2}}) & = & \log_{2} a + \log_{2} b^{2} \\ = & \log_{2} a + 2 \log_{2} b \end{array}$

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