math
posted by kk on .
x lnx  30 + 5 lnx  6x = 0

Are you supposed to solve for x?
(5+x)ln x  6x = 30
That looks to me like a transcendental equation that will have to be solved by iteration or graphing.
Try different values of x on the left side until you get +30.
If x = 0.01, (5+x)ln x  6x = 23.12
If x = 0.05, (5+x)ln x  6x = 15.4
If x = 0.1, (5+x)ln x  6x = 12.3
If x = 1, (5+x)ln x  6x = 6.0
If x = 2, (5+x)ln x  6x = 7.15
If x = 10, (5+x)ln x  6x = 25.6
If x = 20, (5+x)ln x  6x = 45.1
It looks like there is no value of x for which the equation is valid.