Chapter 10: Q. 422 (page 1065)

In the following exercises, use properties of logarithms to write each logarithm as a sum of logarithms. Simplify if possible.
$\log_{3} (\sqrt{4} x^{7} y^{8})$ .

Short Answer

Expert verified

The solution is $\log_{3} (2) + 7 \log_{3} (x) + 8 \log_{3} (y)$ .

Step by step solution

Step 1. Given and explanation.

We have $\log_{3} (\sqrt{4} x^{7} y^{8})$ .

The product property states that if there is an expression as $\log_{a} (m \cdot n)$ , it is equal to $\log_{a} m + \log_{a} n$ .

Applying this, we get the solution.

Step 2. Finding the solution.

We have $\log_{3} (\sqrt{4} x^{7} y^{8})$ .

Applying the product property, we get
$= \log_{3} (\sqrt{4} x^{7} y^{8}) = \log_{3} (\sqrt{4}) + \log_{3} {(x)}^{7} + \log_{3} {(y)}^{8} = \log_{3} (2) + 7 \log_{3} (x) + 8 \log_{3} (y)$
Thus we get the value.

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In the following exercises, use properties of logarithms to write each logarithm as a sum of logarithms. Simplify if possible.
$\log_{3} (\sqrt{4} x^{7} y^{8})$ .

Short Answer

Step by step solution

Step 1. Given and explanation.

Step 2. Finding the solution.

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In the following exercises, use properties of logarithms to write each logarithm as a sum of logarithms. Simplify if possible.log3(4x7y8).

Short Answer

Step by step solution

Step 1. Given and explanation.

Step 2. Finding the solution.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Probability and Statistics

Geometry

Calculus

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Mechanics Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, use properties of logarithms to write each logarithm as a sum of logarithms. Simplify if possible.
$\log_{3} (\sqrt{4} x^{7} y^{8})$ .