Chapter 10: Q. 10.61 (page 1039)

Use the Quotient Property of Logarithms to write each logarithm as a difference of logarithms. Simplify, if
possible.
ⓐ $\log_{4} \frac{3}{4}$
ⓑ $\log (\frac{x}{1000})$

Short Answer

Expert verified

ⓐ logarithm expression $\log_{4} \frac{3}{4}$ as a difference of logarithms is $\log_{4} \frac{3}{4} = \log_{4} 3 - 1$

ⓑ logarithm expression $\log (\frac{x}{1000})$ as a difference of logarithms is $\log (\frac{x}{1000}) = \log x - 3$

Step by step solution

Step 1. given data

Given logarithm expressions are

ⓐ $\log_{4} \frac{3}{4}$

ⓑ $\log (\frac{x}{1000})$

Step 2. part (a)

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

so $\log_{4} \frac{3}{4} = \log_{4} 3 - \log_{4} 4 \log_{4} \frac{3}{4} = \log_{4} 3 - 1$

Step 3. part (b)

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

sorole="math" localid="1644953711368" $\log (\frac{x}{1000}) = \log x - \log 1000 \log (\frac{x}{1000}) = \log x - 3$

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Use the Quotient Property of Logarithms to write each logarithm as a difference of logarithms. Simplify, if
possible.
ⓐ $\log_{4} \frac{3}{4}$
ⓑ $\log (\frac{x}{1000})$

Short Answer

Step by step solution

Step 1. given data

Step 2. part (a)

Step 3. part (b)

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Use the Quotient Property of Logarithms to write each logarithm as a difference of logarithms. Simplify, ifpossible.ⓐ log434ⓑlogx1000

Short Answer

Step by step solution

Step 1. given data

Step 2. part (a)

Step 3. part (b)

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Probability and Statistics

Statistics

Discrete Mathematics

Decision Maths

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Use the Quotient Property of Logarithms to write each logarithm as a difference of logarithms. Simplify, if
possible.
ⓐ $\log_{4} \frac{3}{4}$
ⓑ $\log (\frac{x}{1000})$