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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. 10.61 (page 1039)

Use the Quotient Property of Logarithms to write each logarithm as a difference of logarithms. Simplify, if
possible.
鈸� $\log_{4} \frac{3}{4}$
鈸� $\log (\frac{x}{1000})$

Short Answer

Expert verified

鈸� logarithm expression $\log_{4} \frac{3}{4}$ as a difference of logarithms is $\log_{4} \frac{3}{4} = \log_{4} 3 - 1$

鈸� logarithm expression $\log (\frac{x}{1000})$ as a difference of logarithms is $\log (\frac{x}{1000}) = \log x - 3$

Step by step solution

01

Step 1. given data

Given logarithm expressions are

鈸� $\log_{4} \frac{3}{4}$

鈸� $\log (\frac{x}{1000})$

02

Step 2. part (a)

Use the Quotient Property of logarithm $\log_{a} (\frac{m}{n}) = \log_{a} (m) - \log_{a} (n)$

so $\log_{4} \frac{3}{4} = \log_{4} 3 - \log_{4} 4 \log_{4} \frac{3}{4} = \log_{4} 3 - 1$

03

Step 3. part (b)

Use the Quotient Property of logarithm $\log_{a} (\frac{m}{n}) = \log_{a} (m) - \log_{a} (n)$

sorole="math" localid="1644953711368" $\log (\frac{x}{1000}) = \log x - \log 1000 \log (\frac{x}{1000}) = \log x - 3$

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Most popular questions from this chapter

In the following exercises, solve each logarithmic equation. $y = \log_{1.5} (x)$

In the following exercises, graph each exponential function:

$f (x) = 3^{x + 2}$

In the following exercises, solve each logarithmic equation $y = \log_{0.6} x$

In the following exercises, find the inverse of each function.

$f (x) = 6 x - 7$

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

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

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

See all solutions

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