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Chapter 5: Q 94. (page 309)

Expressy as a function of x. The constant C is a positive number.
$\ln (y + 4) = 5 x + \ln C$

Short Answer

Expert verified

$y = C e^{5 x} - 4$

Step by step solution

Step 1. Given information.

Consider the given information.

$\ln (y + 4) = 5 x + \ln C$

Step 2. Calculation.

Use the logarithm property to solve.

$\begin{array}{l} \ln (y + 4) = 5 x + \ln C \\ \ln (y + 4) - \ln C = 5 x \\ \ln \frac{y + 4}{C} = 5 x \\ \frac{y + 4}{C} = e^{5 x} \\ y + 4 = C e^{5 x} \end{array}$

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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.

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

If $4^{x} = 7$ , what does $4^{- 2 x}$ equal?

The function $f (x) = x^{4}$ is not one-to-one. Find a suitable restriction on the domain of $f$ so that the new function that results is one-to-one. Then find the inverse of $f$ .

The function $f (x) = | x |$ is not one-to-one. Find a suitable restriction on the domain of $f$ so that the new function that results is one-to-one. Then find the inverse of $f$ .

Use transformations to graph the function. Determine the domain, range and horizontal asymptote of the function.

$f (x) = 1 - 2^{- x / 3}$

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Expressy as a function of x. The constant C is a positive number.lny+4=5x+lnC

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Calculation.

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Most popular questions from this chapter

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Expressy as a function of x. The constant C is a positive number.
$\ln (y + 4) = 5 x + \ln C$