Q. 423 In the following exercises, use ... [FREE SOLUTION]

91影视

Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 10: Q. 423 (page 1065)

In the following exercises, use properties of logarithms to write each logarithm as a sum of logarithms. Simplify if possible.
$\log_{5} \frac{8 a^{2} b^{6} c}{d^{3}}$ .

Short Answer

Expert verified

The solution is $3 \log_{5} (2) + 2 \log_{5} (a) + 6 \log_{5} (b) + \log_{5} (c) - 3 \log_{5} (d)$ .

Step by step solution

Step 1. Given and explanation.

We have $\log_{5} \frac{8 a^{2} b^{6} c}{d^{3}}$ .

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

The quotient property states that if there is an expression as $\log_{a} \frac{m}{n}$ , it is equal to $\log_{a} m - \log_{a} n$ .

Applying these properties, we get the solution.

Step 2. Expanding using quotient property.

We have $\log_{5} \frac{8 a^{2} b^{6} c}{d^{3}}$ .

Using the quotient property, we can write this as ,

$\log_{5} (8 a^{2} b^{6} c) - \log_{5} (d^{3})$ .

Step 3. Expanding using product property.

We have $\log_{5} (8 a^{2} b^{6} c) - \log_{5} (d^{3})$ .

Using the product rule, we get
$= \log_{5} (8 a^{2} b^{6} c) - \log_{5} (d^{3}) = [(\log_{5} 8) + (\log_{5} a^{2}) + (\log_{5} b^{6}) + (\log_{5} c)] - \log_{5} (d^{3}) = \log_{5} {(2)}^{3} + \log_{5} {(a)}^{2} + \log_{5} {(b)}^{6} + \log_{5} c - \log_{5} {(d)}^{3} = 3 \log_{5} (2) + 2 \log_{5} (a) + 6 \log_{5} (b) + \log_{5} (c) - 3 \log_{5} (d)$
Thus we get the value.

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91影视

In the following exercises, use properties of logarithms to write each logarithm as a sum of logarithms. Simplify if possible.
$\log_{5} \frac{8 a^{2} b^{6} c}{d^{3}}$ .

Short Answer

Step by step solution

Step 1. Given and explanation.

Step 2. Expanding using quotient property.

Step 3. Expanding using product property.

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91影视

In the following exercises, use properties of logarithms to write each logarithm as a sum of logarithms. Simplify if possible.log58a2b6cd3.

Short Answer

Step by step solution

Step 1. Given and explanation.

Step 2. Expanding using quotient property.

Step 3. Expanding using product property.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Discrete Mathematics

Applied Mathematics

Mechanics Maths

Pure Maths

Statistics

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.
$\log_{5} \frac{8 a^{2} b^{6} c}{d^{3}}$ .