Chapter 11: Q. 10.64 (page 1069)

Use the Power Property of Logarithms to write each logarithm as a product of logarithms. Simplify, if possible.
ⓐ $\log_{2} 3^{7}$ ⓑ $\log x^{20}$

Short Answer

Expert verified

ⓐ logarithm expression $\log_{2} 3^{7}$ as a product of logarithms is $\log_{2} 3^{7} = 7 \cdot \log_{2} 3$

ⓑ logarithm expression $\log x^{20}$ as a product of logarithms is $\log x^{20} = 20 \cdot \log x$

Step by step solution

Step 1. given data

Given logarithm expressions are

ⓐ $\log_{2} 3^{7}$

ⓑ $\log x^{20}$

Step 2. part (a)

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

So $\log_{2} 3^{7} = 7 \cdot \log_{2} 3$

Step 3. part (b)

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

So $\log x^{20} = 20 \cdot \log x$

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Use the Power Property of Logarithms to write each logarithm as a product of logarithms. Simplify, if possible.
ⓐ $\log_{2} 3^{7}$ ⓑ $\log x^{20}$

Short Answer

Step by step solution

Step 1. given data

Step 2. part (a)

Step 3. part (b)

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Use the Power Property of Logarithms to write each logarithm as a product of logarithms. Simplify, if possible.ⓐ log237ⓑ logx20

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

Decision Maths

Statistics

Applied Mathematics

Calculus

Discrete Mathematics

Geometry

Study anywhere. Anytime. Across all devices.

Use the Power Property of Logarithms to write each logarithm as a product of logarithms. Simplify, if possible.
ⓐ $\log_{2} 3^{7}$ ⓑ $\log x^{20}$