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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 95. (page 309)

Expressy as a function of x. The constant C is a positive number.
$3 \ln y = \frac{1}{2} \ln (2 x + 1) - \frac{1}{3} \ln (x + 4) + \ln C$

Short Answer

Expert verified

$y = \sqrt[3]{\frac{C {(2 x + 1)}^{\frac{1}{2}}}{{(x + 4)}^{\frac{1}{3}}}}$

Step by step solution

01

Step 1. Given information.

Consider the given information.

$3 \ln y = \frac{1}{2} \ln (2 x + 1) - \frac{1}{3} \ln (x + 4) + \ln C$

02

Step 2. Calculation.

Use the logarithm property to solve.

$\begin{array}{l} 3 \ln y = \frac{1}{2} \ln (2 x + 1) - \frac{1}{3} \ln (x + 4) + \ln C \\ \ln y^{3} = \ln {(2 x + 1)}^{\frac{1}{2}} - \ln {(x + 4)}^{\frac{1}{3}} + \ln C \\ \ln y^{3} = \ln \frac{{(2 x + 1)}^{\frac{1}{2}}}{{(x + 4)}^{\frac{1}{3}}} + \ln C \\ \ln y^{3} = \ln \frac{C {(2 x + 1)}^{\frac{1}{2}}}{{(x + 4)}^{\frac{1}{3}}} \\ y^{3} = \frac{C {(2 x + 1)}^{\frac{1}{2}}}{{(x + 4)}^{\frac{1}{3}}} \\ y = \sqrt[3]{\frac{C {(2 x + 1)}^{\frac{1}{2}}}{{(x + 4)}^{\frac{1}{3}}}} \end{array}$

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