Q. 467 In the following exercises, use ... [FREE SOLUTION]

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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 10: Q. 467 (page 1068)

In the following exercises, use properties of logarithms to write each expression as a sum of logarithms, simplifying if possible
$\log_{2} \sqrt[4]{\frac{5 x^{3}}{16 y^{2} z^{7}}}$

Short Answer

Expert verified

The value is $\frac{1}{4} \log_{2} 5 + \frac{3}{4} \log_{2} x - 1 - \frac{1}{2} \log_{2} y - \frac{7}{4} \log_{2} z$

Step by step solution

Step 1. Given

An expression is given as $\log_{2} \sqrt[4]{\frac{5 x^{3}}{16 y^{2} z^{7}}}$

Step 2. Calculation

Rewrite the expression as,

$\log_{2} \sqrt[4]{\frac{5 x^{3}}{16 y^{2} z^{7}}} = \log_{2} {(\frac{5 x^{3}}{16 y^{2} z^{7}})}^{\frac{1}{4}} = \frac{1}{4} \log_{2} (\frac{5 x^{3}}{16 y^{2} z^{7}})$

Step 3. Further Calculation

Now use property $\log_{a} \frac{M}{N} = \log_{a} M - \log_{a} N$

$\frac{1}{4} \log_{2} (\frac{5 x^{3}}{2 y^{2} z^{4}}) = \frac{1}{4} (\log_{2} 5 x^{3} - \log_{2} 16 y^{2} z^{7}) = \frac{1}{4} \log_{2} 5 x^{3} - \frac{1}{4} \log_{2} 16 y^{2} z^{7}$

Now use the property $\log_{a} (M 路 N) = \log_{a} M + \log_{a} N$

$\frac{1}{4} \log_{2} (\frac{5 x^{3}}{16 y^{2} z^{7}}) = \frac{1}{4} (\log_{2} 5 + \log_{2} x^{3}) - \frac{1}{4} (\log_{2} 16 + \log_{2} y^{2} + \log_{2} z^{7}) = \frac{1}{4} (\log_{2} 5 + 3 \log_{2} x) - \frac{1}{4} (\log_{2} 2^{4} + 2 \log_{2} y + 7 \log_{2} z) = \frac{1}{4} (\log_{2} 5 + 3 \log_{2} x) - \frac{1}{4} (4 + 2 \log_{2} y + 7 \log_{2} z) = \frac{1}{4} \log_{2} 5 + \frac{3}{4} \log_{2} x - 1 - \frac{1}{2} \log_{2} y - \frac{7}{4} \log_{2} z$

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91影视

In the following exercises, use properties of logarithms to write each expression as a sum of logarithms, simplifying if possible
$\log_{2} \sqrt[4]{\frac{5 x^{3}}{16 y^{2} z^{7}}}$

Short Answer

Step by step solution

Step 1. Given

Step 2. Calculation

Step 3. Further Calculation

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91影视

In the following exercises, use properties of logarithms to write each expression as a sum of logarithms, simplifying if possiblelog25x316y2z74

Short Answer

Step by step solution

Step 1. Given

Step 2. Calculation

Step 3. Further Calculation

One App. One Place for Learning.

Most popular questions from this chapter

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Study anywhere. Anytime. Across all devices.

In the following exercises, use properties of logarithms to write each expression as a sum of logarithms, simplifying if possible
$\log_{2} \sqrt[4]{\frac{5 x^{3}}{16 y^{2} z^{7}}}$