Logarithms

Question

Express each of the following in the form in x=ax + b, and find the value of a and of b.

 

(i) xe^-x =2.46

(ii) (xe^x)² = 30e^-x

 

 

 

Ans:(i) a=1, b= 0.9

       (ii) a= -3/2, b=1.70

 

Thank you :)

Answer 1

"Express each of the following in the form ln(x)=ax + b, and find the value of a and of b."

 

(i) xe^(-x) = 2.46

ln(x) - x(ln(e)) = ln(2.46)

ln(x) - x = ln(2.46)

ln(x) = x + ln(2.46)

a = 1, b = ln(2.46)

(ii) (xe^x)^2 = 30e^(-x)

(x^2)(e^(2x)) = 30e^(-x)

ln(x^2)+ln(e^(2x)) = ln(30) + ln(e^(-x))

2 ln(x) + 2x ln(e) = ln(30) - x ln(e)

2 ln(x) + 2x = ln(30) - x

2 ln(x) = -2x + ln(30) - x

2 ln(x) = -3x + ln(30)

ln(x) = -3x/2 + (ln(30))/2

a = -3/2, b = (ln(30))/2