Solve Exponential Equations

[nycmathguy]

Section 3.4
20, 32, 42

 

[MathLover1]

20. correct but second line is not needed

32.
500e^(-2x)=125

e^(-2x)=125/500

e^(-2x)=1/4

e^(-2x)=4^-2......4^-2=2^-4

ln(e^(-2x))=ln(2^-4)

(-2x)ln(e)=-4ln(2)..............ln(e)=1

-2x=-4ln(2)

x=-4ln(2)/-2

x=2ln(2)-> exact solution

x ≈ 1.38629 -> approximate solution

42. correct

 

[nycmathguy]

20. correct but second line is not needed

32.
500e^(-2x)=125

e^(-2x)=125/500

e^(-2x)=1/4

e^(-2x)=4^-2......4^-2=2^-4

ln(e^(-2x))=ln(2^-4)

(-2x)ln(e)=-4ln(2)..............ln(e)=1

-2x=-4ln(2)

x=-4ln(2)/-2

x=2ln(2)-> exact solution

x ≈ 1.38629 -> approximate solution

42. correct

Well, 2/3 is not too bad. We start trigonometry next week in Chapter 4.