Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 5: Q 100. (page 309)

Find the value of $\log_{2} 2 路 \log_{2} 4 路鈰� 路 \log_{2} 2^{n}$ .

Short Answer

Expert verified

The result is $n!$ .

Step by step solution

Step 1. Given information.

Consider the given expression.

$\log_{2} 2 路 \log_{2} 4 路鈰� 路 \log_{2} 2^{n}$

Step 2. Calculation.

Apply the base change formula to simplify the expression.

$\begin{array}{rcl} \log_{2} 2 路 \log_{2} 4 路鈰� 路 \log_{2} 2^{n} & = & \frac{\log 2}{\log 2} 路 \frac{\log 4}{\log 2} 路鈰� 路 \frac{\log 2^{n}}{\log 2} \\ = & \frac{\log 2^{1}}{\log 2} 路 \frac{\log 2^{2}}{\log 2} 路鈰� 路 \frac{n \log 2}{\log 2} \\ = & 1 路 2 路 3 路鈰� 路 n \\ = & n! \end{array}$

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91影视

Find the value of $\log_{2} 2 路 \log_{2} 4 路鈰� 路 \log_{2} 2^{n}$ .

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Calculation.

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91影视

Find the value oflog22路log24路鈰�路log22n.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Calculation.

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Find the value of $\log_{2} 2 路 \log_{2} 4 路鈰� 路 \log_{2} 2^{n}$ .