Chapter 5: Q 70. (page 309)

Write each expression as a single logarithm.
$3 \log_{5} (3 x + 1) - 2 \log_{5} (2 x - 1) - \log_{5} x$

Short Answer

Expert verified

The result is $\log_{5} [\frac{{(3 x + 1)}^{3}}{{(2 x - 1)}^{2} x}]$ .

Step by step solution

Step 1. Given information.

Consider the given information.

$3 \log_{5} (3 x + 1) - 2 \log_{5} (2 x - 1) - \log_{5} x$

Step 2. Calculation.

Write each expression as a single logarithm.

$\begin{array}{rcl} 3 \log_{5} (3 x + 1) - 2 \log_{5} (2 x - 1) - \log_{5} x & = & \log_{5} {(3 x + 1)}^{3} - \log_{5} {(2 x - 1)}^{2} - \log_{5} x \\ = & \log_{5} {(3 x + 1)}^{3} - [\log_{5} {(2 x - 1)}^{2} + \log_{5} x] \\ = & \log_{5} {(3 x + 1)}^{3} - \log_{5} {(2 x - 1)}^{2} x \\ = & \log_{5} \frac{{(3 x + 1)}^{3}}{{(2 x - 1)}^{2} x} \end{array}$

Step 3. Conclusion.

The obtained result is $\log_{5} \frac{{(3 x + 1)}^{3}}{{(2 x - 1)}^{2} x}$ .

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Write each expression as a single logarithm.
$3 \log_{5} (3 x + 1) - 2 \log_{5} (2 x - 1) - \log_{5} x$

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.3log53x+1-2log52x-1-log5x

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.
$3 \log_{5} (3 x + 1) - 2 \log_{5} (2 x - 1) - \log_{5} x$