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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. 10.66 (page 1041)

Use the Properties of Logarithms to expand the logarithm $\log_{3} (7 x^{5} y^{3})$ . Simplify, if possible.

Short Answer

Expert verified

The expanded form of the logarithm $\log_{3} (7 x^{5} y^{3})$ is $\log_{3} (7 x^{5} y^{3}) = \log_{3} 7 + 5 \log_{3} x + 3 \log_{3} y$

Step by step solution

01

Step 1. given data

Given logarithm expressions is $\log_{3} (7 x^{5} y^{3})$

02

Step 2. Apply product Properties of Logarithms

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

solocalid="1644957182189" $\log_{3} (7 x^{5} y^{3}) = \log_{3} (7) + \log_{3} (x^{5}) + \log_{3} (y^{3})$

03

Step 3. Apply power Property of the logarithm

Use power Property of the logarithm $\log_{a} (m^{p}) = p \log_{a} (m)$

so $\log_{3} (7 x^{5} y^{3}) = \log_{3} (7) + \log_{3} (x^{5}) + \log_{3} (y^{3}) \log_{3} (7 x^{5} y^{3}) = \log_{3} 7 + 5 \log_{3} x + 3 \log_{3} y$

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Most popular questions from this chapter

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

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