Chapter 10: Q. 469 (page 1068)

In the following exercises, use the Properties of Logarithms to condense the logarithm, simplifying if possible.
$\frac{1}{6} \log x - 3 \log (x + 5)$

Short Answer

Expert verified

The simplified expression is $\log \frac{\sqrt[6]{x}}{(x + 5)^{3}}$ .

Step by step solution

Step 1. Given Information

We are given an expression $\frac{1}{6} \log x - 3 \log (x + 5)$ .

Step 2. Solving the expression

Using power property of logarithm, we get

$\frac{1}{6} \log x - 3 \log (x + 5) = \log x^{\frac{1}{6}} - \log (x + 5)^{3}$

Using quotients property of logarithm, we get

localid="1645095131607" $\frac{1}{6} \log x - 3 \log (x + 5) = \log \frac{x^{\frac{1}{6}}}{(x + 5)^{3}} \frac{1}{6} \log x - 3 \log (x + 5) = \log \frac{\sqrt[6]{x}}{(x + 5)^{3}}$

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In the following exercises, use the Properties of Logarithms to condense the logarithm, simplifying if possible.
$\frac{1}{6} \log x - 3 \log (x + 5)$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Solving the expression

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In the following exercises, use the Properties of Logarithms to condense the logarithm, simplifying if possible.16logx-3log(x+5)

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Solving the expression

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Statistics

Calculus

Discrete Mathematics

Theoretical and Mathematical Physics

Decision Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, use the Properties of Logarithms to condense the logarithm, simplifying if possible.
$\frac{1}{6} \log x - 3 \log (x + 5)$