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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. 10.69 (page 1042)

Use the Properties of Logarithms to condense the logarithm $\log_{2} 5 + \log_{2} x - \log_{2} y$ . Simplify, if possible.

Short Answer

Expert verified

The condensed form of the logarithm is $\log_{2} 5 + \log_{2} x - \log_{2} y = \log_{2} \frac{5 x}{y}$

Step by step solution

01

Step 1. given data

Given logarithm expressions is $\log_{2} 5 + \log_{2} x - \log_{2} y$

02

Step 2. Apply product Property of the logarithm

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

role="math" localid="1644961031838" $\log_{2} 5 + \log_{2} x - \log_{2} y = \log_{2} 5 x - \log_{2} y$

03

Step 3. apply Quotient Property of logarithm

Use Quotient Property of the logarithm $\log_{a} (m) - \log_{a} (n) = \log_{a} (\frac{m}{n})$

$\log_{2} 5 + \log_{2} x - \log_{2} y = \log_{2} 5 x - \log_{2} y \log_{2} 5 + \log_{2} x - \log_{2} y = \log_{2} \frac{5 x}{y}$

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