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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. 10.65 (page 1041)

Use the Properties of Logarithms to expand the logarithm $\log_{2} (5 x^{4} y^{2})$ . Simplify, if possible

Short Answer

Expert verified

The expanded form of the logarithm $\log_{2} (5 x^{4} y^{2})$ is $\log_{2} (5 x^{4} y^{2}) = \log_{2} (5) + 4 \log_{2} (x) + 2 \log_{2} (y)$

Step by step solution

01

Step 1. given data

Given logarithm expressions is $\log_{2} (5 x^{4} y^{2})$

02

Step 2. Apply product Properties of Logarithms

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

sorole="math" localid="1644956884292" $\log_{2} (5 x^{4} y^{2}) = \log_{2} (5) + \log_{2} (x^{4}) + \log_{2} (y^{2})$

03

Step 3. Apply power Property of the logarithm

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

so $\log_{2} (5 x^{4} y^{2}) = \log_{2} (5) + \log_{2} (x^{4}) + \log_{2} (y^{2}) \log_{2} (5 x^{4} y^{2}) = \log_{2} (5) + 4 \log_{2} (x) + 2 \log_{2} (y)$

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Most popular questions from this chapter

Convert from exponential to logarithmic form:

$3^{- 2} = \frac{1}{9}$ .

Convert from exponential to logarithmic form:

$10^{- 2} = \frac{1}{100}$ .

Graph: $g (x) = {(\frac{1}{5})}^{x}$

For functions $f (x) = 4 x - 3$ and

$g (x) = 6 x - 5$ , find

$(f 鈭� g) (x)$
$(g 鈭� f) (x)$
$(f 路 g) (x)$

Find the inverse of the function , $f (x) = \sqrt[5]{3 x - 2}$

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