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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 91. (page 309)

Expressy as a function of x. The constant C is a positive number.
$\ln y = 3 x + \ln C$

Short Answer

Expert verified

$y = C e^{3 x}$

Step by step solution

01

Step 1. Given information.

Consider the given information.

$\ln y = 3 x + \ln C$

02

Step 2. Calculation.

Use the logarithm property to solve.

$\begin{array}{rcl} \ln y & = & 3 x + \ln C \\ \ln y - \ln C & = & 3 x \\ \ln \frac{y}{C} & = & 3 x \\ \frac{y}{C} & = & e^{3 x} \\ y & = & C e^{3 x} \end{array}$

03

Step 3. Conclusion.

The result is $y = C e^{3 x}$ .

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