Chapter 10: Q. 10.66 (page 1041)

Use the Properties of Logarithms to expand the logarithm $\log_{3} (7 x^{5} y^{3})$ . Simplify, if possible.

Short Answer

Expert verified

The expanded form of the logarithm $\log_{3} (7 x^{5} y^{3})$ is $\log_{3} (7 x^{5} y^{3}) = \log_{3} 7 + 5 \log_{3} x + 3 \log_{3} y$

Step by step solution

Step 1. given data

Given logarithm expressions is $\log_{3} (7 x^{5} y^{3})$

Step 2. Apply product Properties of Logarithms

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

solocalid="1644957182189" $\log_{3} (7 x^{5} y^{3}) = \log_{3} (7) + \log_{3} (x^{5}) + \log_{3} (y^{3})$

Step 3. Apply power Property of the logarithm

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

so $\log_{3} (7 x^{5} y^{3}) = \log_{3} (7) + \log_{3} (x^{5}) + \log_{3} (y^{3}) \log_{3} (7 x^{5} y^{3}) = \log_{3} 7 + 5 \log_{3} x + 3 \log_{3} y$

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Use the Properties of Logarithms to expand the logarithm $\log_{3} (7 x^{5} y^{3})$ . Simplify, if possible.

Short Answer

Step by step solution

Step 1. given data

Step 2. Apply product Properties of Logarithms

Step 3. Apply power Property of the logarithm

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Use the Properties of Logarithms to expand the logarithmlog37x5y3. Simplify, if possible.

Short Answer

Step by step solution

Step 1. given data

Step 2. Apply product Properties of Logarithms

Step 3. Apply power Property of the logarithm

One App. One Place for Learning.

Most popular questions from this chapter

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Use the Properties of Logarithms to expand the logarithm $\log_{3} (7 x^{5} y^{3})$ . Simplify, if possible.