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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. 268 (page 1045)

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

Short Answer

Expert verified

On simplifying the expression we get: $\log_{7} (\frac{3 x}{y})$

Step by step solution

01

Step 1. Given information

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

We have to condense the expression using logarithm properties.

02

Step 2. Use product property of logarithm

Use product property of logarithm which states:

$\log_{a} M + \log_{a} N = \log_{a} (M 路 N)$

03

Step 3. Apply the product property of logarithm on the first two terms.

$\log_{7} 3 + \log_{7} x - \log_{7} y = \log_{7} 3 x - \log_{7} y$

04

Step 4. Use quotient property of logarithm

Use quotient property of logarithm which states:

$\log_{a} M - \log_{a} N = \log_{a} (\frac{M}{N})$

05

Step 5. Apply the quotient property of logarithm

$\log_{7} 3 x - \log_{7} y = \log_{7} (\frac{3 x}{y})$

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Most popular questions from this chapter

In the following exercises, graph each function in the same coordinate system:

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