Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 5: Q 97. (page 309)

Find the value of $\log_{2} 3 路 \log_{3} 4 路 \log_{4} 5 路 \log_{5} 6 路 \log_{6} 7 路 \log_{7} 8$ .

Short Answer

Expert verified

The obtained result is 3.

Step by step solution

Step 1. Given information.

Consider the given expression.

$\log_{2} 3 路 \log_{3} 4 路 \log_{4} 5 路 \log_{5} 6 路 \log_{6} 7 路 \log_{7} 8$

Step 2. Calculation.

Apply the base change formula to simplify the expression.

$\begin{array}{rcl} \log_{2} 3 路 \log_{3} 4 路 \log_{4} 5 路 \log_{5} 6 路 \log_{6} 7 路 \log_{7} 8 & = & \frac{\log 3}{\log 2} 路 \frac{\log 4}{\log 3} 路 \frac{\log 5}{\log 4} 路 \frac{\log 6}{\log 5} 路 \frac{\log 7}{\log 6} 路 \frac{\log 8}{\log 7} \\ = & \frac{1}{\log 2} 路 \frac{1}{1} 路 \frac{1}{1} 路 \frac{1}{1} 路 \frac{1}{1} 路 \frac{\log 2^{3}}{1} \\ = & \frac{3 \log 2}{\log 2} \\ = & 3 \end{array}$

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91影视

Find the value of $\log_{2} 3 路 \log_{3} 4 路 \log_{4} 5 路 \log_{5} 6 路 \log_{6} 7 路 \log_{7} 8$ .

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Calculation.

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91影视

Find the value oflog23路log34路log45路log56路log67路log78.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Calculation.

One App. One Place for Learning.

Most popular questions from this chapter

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Find the value of $\log_{2} 3 路 \log_{3} 4 路 \log_{4} 5 路 \log_{5} 6 路 \log_{6} 7 路 \log_{7} 8$ .