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Chapter 5: Q 92. (page 309)

Expressy as a function ofx. The constantC is a positive number.
$\ln y = - 2 x + \ln C$

Short Answer

Expert verified

$y = C e^{- 2 x}$

Step by step solution

Step 1. Given information.

Consider the given information.

$\ln y = - 2 x + \ln C$

Step 2. Calculation.

Use the logarithm property to solve.

$\begin{array}{l} \ln y = - 2 x + \ln C \\ \ln y - \ln C = - 2 x \\ \ln \frac{y}{C} = - 2 x \\ \frac{y}{C} = e^{- 2 x} \\ y = C e^{- 2 x} \end{array}$

Step 3. Conclusion.

The obtained result is $y = C e^{- 2 x}$ .

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Expressy as a function ofx. The constantC is a positive number.lny=-2x+lnC

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Calculation.

Step 3. Conclusion.

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Expressy as a function ofx. The constantC is a positive number.
$\ln y = - 2 x + \ln C$