Chapter 10: Q. 10.71 (page 1042)

Use the Properties of Logarithms to condense the logarithm $3 \log_{2} x + 2 \log_{2} (x - 1)$ . Simplify, if possible.

Short Answer

Expert verified

The condensed form of the logarithm is $3 \log_{2} x + 2 \log_{2} (x - 1) = \log_{2} x^{3} {(x - 1)}^{2}$

Step by step solution

Step 1. given data

Given logarithm expressions is $3 \log_{2} x + 2 \log_{2} (x - 1)$

Step 2. Apply power Property of the logarithm

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

role="math" localid="1644962279660" $3 \log_{2} x + 2 \log_{2} (x - 1) = \log_{2} x^{3} + \log_{2} {(x - 1)}^{2}$

Step 3. apply product Properties of Logarithms

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

$3 \log_{2} x + 2 \log_{2} (x - 1) = \log_{2} x^{3} + \log_{2} {(x - 1)}^{2} 3 \log_{2} x + 2 \log_{2} (x - 1) = \log_{2} x^{3} {(x - 1)}^{2}$

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Use the Properties of Logarithms to condense the logarithm $3 \log_{2} x + 2 \log_{2} (x - 1)$ . Simplify, if possible.

Short Answer

Step by step solution

Step 1. given data

Step 2. Apply power Property of the logarithm

Step 3. apply product Properties of Logarithms

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Use the Properties of Logarithms to condense the logarithm 3log2x+2log2x-1. Simplify, if possible.

Short Answer

Step by step solution

Step 1. given data

Step 2. Apply power Property of the logarithm

Step 3. apply product Properties of Logarithms

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Geometry

Calculus

Probability and Statistics

Discrete Mathematics

Pure Maths

Study anywhere. Anytime. Across all devices.

Use the Properties of Logarithms to condense the logarithm $3 \log_{2} x + 2 \log_{2} (x - 1)$ . Simplify, if possible.