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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 5: Q 22. (page 308)

Use properties of logarithms to find the exact value of each expression. Do not use a calculator.
$\log_{8} 16 - \log_{8} 2$

Short Answer

Expert verified

The value is 1.

Step by step solution

01

Step 1. Given information.

Consider the given information.

$\log_{8} 16 - \log_{8} 2$

02

Step 2. Logarithm properties.

The properties are defined as,

$\begin{array}{l} \log_{a} a = 1 \\ \log_{a} (\frac{M}{N}) = \log_{a} M - \log_{a} N \\ \log_{a} M^{r} = r \log_{a} M \end{array}$

03

Step 3. Calculation.

Apply the properties.

$\begin{array}{rcl} \log_{8} 16 - \log_{8} 2 & = & \log_{8} (\frac{16}{2}) \\ = & \log_{8} (8) \\ = & 1 \end{array}$

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Most popular questions from this chapter

Solve given equation and verify your result using graphing utility.

${(e^{4})}^{x} . e^{x}$ ²=e12

The function $f (x) = x^{4}$ is not one-to-one. Find a suitable restriction on the domain of $f$ so that the new function that results is one-to-one. Then find the inverse of $f$ .

In Problems $33 - 40$ , the graph of an exponential function is given. Match each graph to one of the following functions.

Determine the exponential function whose graph is given.

Answers are given at the end of these exercises. If you get a wrong answer, read the pages listed in red.

Solve:

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