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Chapter 5: Q 107. (page 299)

Solve the equation.

Short Answer

Expert verified

The solution to the equation,

5e0.2x=7

Step by step solution

01

Step 1. Given Information 

The given equation to be solved is 5e0.2x=7is, x=5ln75.

02

Step 2. Formula used

Natural logarithm:

lne=1

03

Step 3. Finding Solution

The given equation is 5e0.2x=7.

Divide both sides by 5.

5e0.2x5=75

e0.2x=75

Take logarithm on both sides.

lne0.2x=ln75

0.2xlne=ln75

0.2x=ln75

x=5ln75

The solution to the given equationis,x=5ln75.

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Most popular questions from this chapter

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

f(x)=-3x+1x

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

True or False

The function f(x)=2xx-3 hasy=2 as a horizontal asymptote.

Vehicle Stopping Distance Taking into account reaction time, the distance d(in feet) that a car requires to come to a complete stop while traveling rmiles per hour is given by the function

localid="1646198784356" d(r)=6.97r-90.39

a. Express the speed rat which the car is traveling as a function of the distance localid="1646198792401" drequired to come to a complete stop

b. Verify that localid="1646198797631" r=r(d)is the inverse of localid="1646198802104" d=d(r)by showing that localid="1646198806352" r(d(r))=rand localid="1646198811055" d(r(d))=d

c. Predict the speed that a car was traveling if the distance required to stop was localid="1646198818232" 300feet.

d(r(d))=d

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

f(x)=2x+3x+2

Find f(3x)iff(x)=4-2x2.
See all solutions

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