math

posted by .

1.Express (xe^x)^2=30e^(-x) in the form lnx=ax+b,and find the value of a and of b .

2.solve 4(3^2x)=e^x

  • math -

    1. take ln of both sides

    ln(x e^x)^2 = ln(30 e^-x)
    2 lnx + 2ln e^x = ln30 + ln e^-x
    2lnx + 2x = ln30 -x
    2 lnx = -3x + ln30
    lnx = (-3/2)x + (1/2)ln30 or (-3/2)x + ln (√30)
    comparing this with ax + b
    a = -3/2 , b = ln √30

    2. take ln of both sides and use rules of logs

    ln (4(3^2x) ) = ln e^x
    ln4 + xln3 = x
    x - 2xln3 = ln4
    x(1 - 2ln3) = ln4
    x = ln4/(1-2ln3) or appr. -1.1579

    check:
    LS = 4(3^-2.3158... = .31413784
    RS = e^-1.157923.. = .31413784 , how about that?

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Math (Calculus)

    Can somebody solve this logarithm problem step by step for me please: 2(lnx)² + lnx-1 = 0 First let y = ln x be a new variable, , and solve the polynomial 2 y^2 + y - 1 = 0 2(y +1)(y - 1/2) = 0 Solutions are y = -1 or +1/2 Thus x …
  2. math

    how would you solve for y in this problem: ln(y-1)-ln2 = x +lnx ln(y-1)-ln2 = x +lnx Solve for y... ln[(y-1)/2]]=x + lnx take the antilog of each side (y-1)/2= e^(x+lnx) solve for y.
  3. algebra 2

    Would some one look at these problems and see if I got them right Thanks Just let me if they are wrong so I can go back over them 1.Write in simplest form 48/56 A. 6/7 2.Multiply 8x^3/5 *10/x^3 A. 16/x^4 3.Divide 4/x^7 / 12/x^3 A. …
  4. math

    I am suppose to simplify the following problems: sqrt(x)/x (isn't that already simplified?
  5. statistics

    Does anyone know how to solve these two problems. Solve the problem. Find the critical value za/2 that corresponds to a degree of condfidence of 98%. Express the confidence interval in the form of ^p _+E. 0.033<p>0.493
  6. calculus

    (a) find the intervals on which f is incrs or decrs. (b) find the local min/max values of f. (c) find the intervals of concavity and the inflection points. f(x)=(lnx)/sqrtx I took the derivative and got 2-lnx/2x^3/2 take the values …
  7. Math logs

    Solve the system of equations: y= (lnx)^2 + 2 (lnx^2) y = 3ln(1/x^2)+24 Im not sure what to do..
  8. Math

    I cant figure this question out. I could use some help. Solve for x lnx-lnx^2+ln5 = 0 Simplify the answer
  9. L'Hopital's rule

    Find lim x->1+ of [(1/(x-1))-(1/lnx)]. Here is my work... =(lnx-(x-1)) / ((x-1)(lnx)) =(lnx-1) / (lnx+ (x+1)/x) This becomes(1/x) / ((1/x)+(1/x^2)) which becomes 1/ (1/x^2) This equals 1/2. I understand the answer has to be -1/2, …
  10. Calculus 1

    Find the derivative of y with respect to x. y=(x^6/6)(lnx)-(x^6/36) So far this is what I've gotten: y=(x^6/6)(lnx)-(x^6/36) y=(1/6)x^6(lnx)-(1/36)x^6 y'=(1/6)x^5(1/x)+lnx(x^5)-(1/6)x^5 What do I do now?

More Similar Questions