Posted by **Mike** on Wednesday, October 14, 2009 at 12:53am.

Solve the system of equations:

y= (lnx)^2 + 2 (lnx^2)

y = 3ln(1/x^2)+24

Im not sure what to do..

- Math logs -
**Reiny**, Wednesday, October 14, 2009 at 8:28am
so we equate the two

(lnx)^2 + 2(lnx^2) = 3ln(1/x^2)+24

now some preliminary calculations:

(lnx^2) = 2lnx

so 2(lnx^2) = 4lnx

and

ln(1/x^2) = ln1 - lnx^2

= 0 - 2lnx = - 2lnx

so our equation becomes

(lnx)^2 + 4lnx = 6lnx + 24

let lnx = t

so we have

t^2 - 2t - 24 = 0

(t-6)(t+4) = 0

t = 6 or t = -4

then lnx = 6 or lnx = -4

but the second of those of course is undefined, so

lnx = 6

x = e^6

## Answer This Question

## Related Questions

- math - how would you solve for y in this problem: ln(y-1)-ln2 = x +lnx ln(y-1)-...
- L'Hopital's rule - Find lim x->1+ of [(1/(x-1))-(1/lnx)]. Here is my work...
- calculus - sorry to ask a second question so soon, but i'm just not getting this...
- Calculus 1 - Find the derivative of y with respect to x. y=(x^6/6)(lnx)-(x^6/36...
- Calculus - what is the limit as h approaches 0 of ((x+h)^pi-x^pi)/h? Multiple ...
- math - I am suppose to simplify the following problems: sqrt(x)/x (isn't that ...
- calc - integral of 1 to e^4 dx/x(1+lnx) 1+lnx = a => dx/x = da dx/ x(1+lnx...
- Calculus - Find the derivatives, dy/dx for the following functions. a. x^2y^4 = ...
- Math - I cant figure this question out. I could use some help. Solve for x lnx-...
- calculus - (a) find the intervals on which f is incrs or decrs. (b) find the ...

More Related Questions