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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 9. (page 309)

$M = \frac{\log_{5} 7}{\log_{5} 8}$

Short Answer

Expert verified

The obtained value is $\begin{array}{rcl} \log_{8} 7 \end{array}$ .

Step by step solution

Step 1. Given information.

Consider the given information.

$M = \frac{\log_{5} 7}{\log_{5} 8}$

Step 2. Calculation.

Apply the base change property.

$\begin{array}{rcl} M & = & \frac{\log_{5} 7}{\log_{5} 8} \\ = & \frac{\frac{\log 7}{\log 5}}{\frac{\log 8}{\log 5}} \\ = & \frac{\log 7}{\log 5} 路 \frac{\log 5}{\log 8} \\ = & \frac{\log 7}{\log 8} \\ = & \frac{\log 7}{\log 8} \\ = & \log_{8} 7 \end{array}$

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M=log57log58

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Calculation.

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$M = \frac{\log_{5} 7}{\log_{5} 8}$