Chapter 10: Q. 10.70 (page 1042)

Use the Properties of Logarithms to condense the logarithm $\log_{3} 6 - \log_{3} x - \log_{3} y$ . Simplify, if possible.

Short Answer

Expert verified

The condensed form of the logarithm is $\log_{3} 6 - \log_{3} x - \log_{3} y = \log_{3} \frac{6}{x y}$

Step by step solution

Step 1. given data

Given logarithm expressions is $\log_{3} 6 - \log_{3} x - \log_{3} y$

Step 2. Apply product Property of the logarithm

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

$\log_{3} 6 - \log_{3} x - \log_{3} y = \log_{3} 6 - (\log_{3} x + \log_{3} y) \log_{3} 6 - \log_{3} x - \log_{3} y = \log_{3} 6 - \log_{3} x y$

Step 3. apply Quotient Property of logarithm

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

role="math" localid="1644961515813" $\log_{3} 6 - \log_{3} x - \log_{3} y = \log_{3} 6 - \log_{3} x y \log_{3} 6 - \log_{3} x - \log_{3} y = \log_{3} \frac{6}{x y}$

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Use the Properties of Logarithms to condense the logarithm $\log_{3} 6 - \log_{3} x - \log_{3} y$ . Simplify, if possible.

Short Answer

Step by step solution

Step 1. given data

Step 2. Apply product Property of the logarithm

Step 3. apply Quotient Property of logarithm

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Use the Properties of Logarithms to condense the logarithm log36-log3x-log3y. Simplify, if possible.

Short Answer

Step by step solution

Step 1. given data

Step 2. Apply product Property of the logarithm

Step 3. apply Quotient Property of logarithm

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Applied Mathematics

Pure Maths

Discrete Mathematics

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Probability and Statistics

Study anywhere. Anytime. Across all devices.

Use the Properties of Logarithms to condense the logarithm $\log_{3} 6 - \log_{3} x - \log_{3} y$ . Simplify, if possible.