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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 24. (page 308)

Use properties of logarithms to find the exact value of each expression. Do not use a calculator.
$\log_{3} 8 路 \log_{8} 9$

Short Answer

Expert verified

The value is 2.

Step by step solution

01

Step 1. Given information.

Consider the given information,

$\log_{3} 8 路 \log_{8} 9$

02

Step 2. Logarithm properties.

The properties are defined as,

$\begin{array}{l} \log_{a} b = \frac{\log b}{\log a} \\ \log_{a} M^{r} = r \log_{a} M \end{array}$

03

Step 3. Calculation.

Apply the properties,

$\begin{array}{l} \log_{3} 8 路 \log_{8} 9 = \frac{\log 8}{\log 3} 路 \frac{\log 9}{\log 8} \\ = \frac{\log 9}{\log 3} \\ = \frac{\log 3^{2}}{\log 3} \\ = \frac{2 \log 3^{2}}{\log 3} \\ = 2 \end{array}$

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Most popular questions from this chapter

If $2^{x} = 3$ , what does $4^{- x}$ equal?

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