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

Step 1. Given information.

Consider the given information.

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

Step 2. Calculation.

Apply the logarithm properties to combine the terms.

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

Step 3. Conclusion.

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

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

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Calculation.

Step 3. Conclusion.

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Write each expression as a single logarithm.21log3x3+log39x2-log39

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Calculation.

Step 3. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

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