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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 66. (page 309)

Write each expression as a single logarithm.
$21 \log_{3} \sqrt[3]{x} + \log_{3} (9 x^{2}) - \log_{3} 9$

Short Answer

Expert verified

The result is $\begin{array}{rcl} 9 \log_{3} x \end{array}$ .

Step by step solution

01

Step 1. Given information.

Consider the given information.

$21 \log_{3} \sqrt[3]{x} + \log_{3} (9 x^{2}) - \log_{3} 9$

02

Step 2. Calculation.

Apply the logarithm properties to combine the terms.

$\begin{array}{rcl} 21 \log_{3} \sqrt[3]{x} + \log_{3} (9 x^{2}) - \log_{3} 9 & = & 21 \log_{3} {(x)}^{\frac{1}{3}} + \log_{3} 9 + \log_{3} x^{2} - \log_{3} 9 \\ = & \frac{21}{3} \log_{3} x + 2 \log_{3} x \\ = & 7 \log_{3} x + 2 \log_{3} x \\ = & 9 \log_{3} x \end{array}$

03

Step 3. Conclusion.

The obtained result is $\begin{array}{rcl} 9 \log_{3} x \end{array}$ .

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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.

Solve the equation ${(\frac{1}{4})}^{x} = \frac{1}{64}$

and verify your results using a graphing utility.

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

$f (x) = \frac{2 x}{3 x - 1}$

If $f (7) = 3$ and f is one-to-one, what is $f^{- 1} (13)$ ?

Do you think that there is a power function that increases

more rapidly than an exponential function whose base is greater than 1 ? Explain.

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