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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 45. (page 308)

Write each expression as a sum and/or difference of logarithms. Express powers as factors.
$\log_{a} (u^{2} v^{3})$

Short Answer

Expert verified

The result is $2 \log_{a} u + 3 \log_{a} v$ .

Step by step solution

01

Step 1. Given information.

Consider the given information.

$\log_{a} (u^{2} v^{3})$

02

Step 2. Formula used.

The logarithm properties are defined as,

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

03

Step 2. Calculation.

Apply the logarithm property to simplify.

$\begin{array}{rcl} \log_{a} (u^{2} v^{3}) & = & \log_{a} u^{2} + \log_{a} v^{3} \\ = & 2 \log_{a} u + 3 \log_{a} v \end{array}$

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Most popular questions from this chapter

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