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Chapter 5: Q 87. (page 309)

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

Short Answer

Expert verified

$y = C x$

Step by step solution

01

Step 1. Given information.

Consider the given information.

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

02

Step 2. Calculation.

Use the logarithm property to solve.

$\begin{array}{rcl} \ln y & = & \ln x + \ln C \\ \ln y & = & \ln x C \\ y & = & x C \end{array}$

03

Step 3. Conclusion.

The result is $y = C x$ .

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Most popular questions from this chapter

In Problems 61–72, the function f is one-to-one. Find its inverse and check your answer.

$f (x) = \frac{3 x + 4}{2 x - 3}$

Solve the equation. Verify your results using a graphing utility.

$7^{x} = 7^{3}$

Begin with the graph of $y = e^{x}$ and use transformation to graph the function. Determine the domain, range and horizontal asymptote of the function.

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Answers are given at the end of these exercises. If you get a wrong answer, read the pages listed in red.

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In Problems 61–72, the function f is one-to-one. Find its inverse and check your answer.

$f (x) = - \frac{3 x + 1}{x}$

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