Chapter 5: Q 65. (page 309)

Write each expression as a single logarithm.
$8 \log_{2} \sqrt{3 x - 2} - \log_{2} (\frac{4}{x}) + \log_{2} 4$

Short Answer

Expert verified

The result is $\begin{array}{rcl} \log_{2} [x {(3 x - 2)}^{4}] \end{array}$ .

Step by step solution

Step 1. Given information.

Consider the given expression.

$8 \log_{2} \sqrt{3 x - 2} - \log_{2} (\frac{4}{x}) + \log_{2} 4$

Step 2. Calculation.

Apply the logarithm properties to combine the terms.

$\begin{array}{rcl} 8 \log_{2} \sqrt{3 x - 2} - \log_{2} (\frac{4}{x}) + \log_{2} 4 & = & 8 \log_{2} {(3 x - 2)}^{\frac{1}{2}} - \log_{2} 4 + \log_{2} x + \log_{2} 4 \\ = & \log_{2} {(3 x - 2)}^{\frac{8}{2}} + \log_{2} x \\ = & \log_{2} [x {(3 x - 2)}^{4}] \end{array}$

Step 3. Conclusion.

The obtained result is $\log_{2} \frac{{(3 x - 2)}^{4}}{x}$ .

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Write each expression as a single logarithm.
$8 \log_{2} \sqrt{3 x - 2} - \log_{2} (\frac{4}{x}) + \log_{2} 4$

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.8log23x-2-log24x+log24

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.
$8 \log_{2} \sqrt{3 x - 2} - \log_{2} (\frac{4}{x}) + \log_{2} 4$