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Chapter 5: Q 98. (page 309)

Find the value of $\log_{2} 4 \cdot \log_{4} 6 \cdot \log_{6} 8$ .

Short Answer

Expert verified

The obtained result is 3.

Step by step solution

01

Step 1. Given information.

Consider the given expression.

$\log_{2} 4 \cdot \log_{4} 6 \cdot \log_{6} 8$

02

Step 2. Calculation.

Apply the base change formula to simplify the expression.

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

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Most popular questions from this chapter

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

In Problems 61–72, the function f is one-to-one. Find its inverse and check your answer.

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Begin with the graph of $y = e^{x}$ and use transformation to graph the function. Determine the domain, range and horizontal asymptote of the function.

$f (x) = e^{- x}$

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