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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. 10.60 (page 1038)

Use the Product Property of Logarithms to write each logarithm as a sum of logarithms. Simplify, if possible.
鈸� $\log_{9} (9 x)$ 鈸� $\log_{3} (27 x y)$

Short Answer

Expert verified

鈸� logarithm expression $\log_{9} (9 x)$ as the sum of logarithms is $\log_{9} (9 x) = 1 + \log_{9} x$

鈸� logarithm expression $\log_{3} (27 x y)$ as the sum of logarithms is $\log_{3} (27 x y) = 3 + \log_{3} x + \log_{3} y$

Step by step solution

01

Step 1. given data

Given logarithm expressions are

鈸� $\log_{9} (9 x)$

鈸� $\log_{3} (27 x y)$

02

Step 2. part (a)

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

so $\log_{9} (9 x) = \log_{9} (9 路 x) \log_{9} (9 x) = \log_{9} 9 + \log_{9} x \log_{9} (9 x) = 1 + \log_{9} x$

03

Step 3. part (b)

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

so

$\log_{3} (27 x y) = \log_{3} (27 路 x 路 y) \log_{3} (27 x y) = \log_{3} 27 + \log_{3} x + \log_{3} y \log_{3} (27 x y) = \log_{3} 3^{3} + \log_{3} x + \log_{3} y \log_{3} (27 x y) = 3 + \log_{3} x + \log_{3} y$

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Most popular questions from this chapter

In the following exercises, find

a. $f 鈭� g (x)$

b. $g 鈭� f (x)$

c. $(f . g) (x)$

$f (x) = 3 x - 1 g (x) = 5 x - 3$

In the following exercises, find the inverse of each function.

$f (x) = - 2 x + 5$

Edgar accumulated $$ 5000$ in credit card debt. If the interest rate is $20 %$ per year, and he does not make any payments for $2$ years, how much will he owe on this debt in $2$ years by each method of compounding?

a. compound quarterly

b. compound monthly

c. compound continuously.

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

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

In the following exercises, find the inverse of each function.

$f (x) = 8 x$

See all solutions

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