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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 10: Q. 10.59 (page 1038)

Use the Product Property of Logarithms to write each logarithm as a sum of logarithms. Simplify, if possible.
鈸� $\log_{3} 3 x$ 鈸� $\log_{2} 8 x y$

Short Answer

Expert verified

鈸� logarithm expression $\log_{3} 3 x$ as the sum of logarithms isrole="math" localid="1644951471169" $\log_{3} 3 x = 1 + \log_{3} x$

鈸� logarithm expression $\log_{2} 8 x y$ as the sum of logarithms is $\log_{2} 8 x y = 3 + \log_{2} x + \log_{2} y$

Step by step solution

01

Step 1. given data

Given logarithm expressions are

鈸� $\log_{3} 3 x$

鈸� $\log_{2} 8 x y$

02

Step 2. part (a)

Use product Properties of Logarithms $\log_{a} (m 路 n) = \log_{a} m + \log_{a} n$

so $\log_{3} 3 x = \log_{3} (3 路 x) \log_{3} 3 x = \log_{3} 3 + \log_{3} x \log_{3} 3 x = 1 + \log_{3} x$

03

Step 3. part (b)

Use product Properties of Logarithms $\log_{a} (m 路 n) = \log_{a} m + \log_{a} n$

sorole="math" localid="1644951807515" $\log_{2} 8 x y = \log_{2} (8 路 x 路 y) \log_{2} 8 x y = \log_{2} 8 + \log_{2} x + \log_{2} y \log_{2} 8 x y = \log_{2} 2^{3} + \log_{2} x + \log_{2} y \log_{2} 8 x y = 3 + \log_{2} x + \log_{2} y$

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Most popular questions from this chapter

Find the inverse of the function , $f (x) = 8 x + 5$

In the following exercises, match the graphs to one of the following functions:

$鈸� 2^{x} 鈸� 2^{x + 1} 鈸� 2^{x - 1} 鈸� 2^{x} + 2 鈸� 2^{x} 鈭� 2 鈸� 3^{x}$

Convert each logarithmic equation to exponential form:

$3 = \log_{4} (64)$ .

In the following exercises, solve each equation.

$3^{x^{2} - 2 x} = \frac{1}{3}$

Graph: $g (x) = {(\frac{1}{5})}^{x}$

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