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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. 468 (page 1068)

In the following exercises, use the Properties of Logarithms to condense the logarithm, simplifying if possible.
$5 \log_{4} x + 3 \log_{4} y$

Short Answer

Expert verified

The value is $\log_{4} x^{5} y^{3}$

Step by step solution

01

Step 1. Given

An expression is given as $5 \log_{4} x + 3 \log_{4} y$

02

Step 2. Calculation

Use property $\log_{a} M^{p} = p \log_{a} M$ ,

$5 \log_{4} x + 3 \log_{4} y = \log_{4} x^{5} + \log_{4} y^{3}$

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

$5 \log_{4} x + 3 \log_{4} y = \log_{4} x^{5} y^{3}$

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