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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 96. (page 309)

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

Short Answer

Expert verified

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

Step by step solution

01

Step 1. Given information.

Consider the given information.

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

02

Step 2. Calculation.

Use the logarithm property to solve.

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

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