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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. 427 (page 1065)

In the following exercises, use the Properties of Logarithms to condense the logarithm. Simplify if possible.
$3 \log_{3} x + 7 \log_{3} y$

Short Answer

Expert verified

a condensed form of the logarithm is $3 \log_{3} x + 7 \log_{3} y = \log_{3} (x^{3} y^{7})$

Step by step solution

01

Step 1. Given data

The given logarithm expression is $3 \log_{3} x + 7 \log_{3} y$

02

Step 2. Apply the power properties of the logarithm

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

role="math" localid="1645030581888" $3 \log_{3} x + 7 \log_{3} y = \log_{3} x^{3} + \log_{3} y^{7}$

03

Step 3. Apply the product properties of the logarithm

Use product properties of the logarithm $\log_{a} (m n) = \log_{a} (m) + \log_{a} (n)$

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

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Most popular questions from this chapter

In the following exercises, solve each equation.

$\frac{e^{x^{2}}}{e^{3}} = e^{2 x}$

Convert from exponential to logarithmic form:

$x^{\frac{1}{2}} = \sqrt{3}$ .

In the following exercises, graph each exponential function.

$g (x) = 7^{x}$

Convert each logarithmic equation to exponential form:

$3 = \log_{4} (64)$ .

In the following exercises, find the inverse of each function. Determine the domain and range of the inverse function.
$\{(5, 3), (4, 2), (3, 1), (2, 0)\}$ .

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