Question

Solve the following equation for x:
ln(2-x)+ ln(3x)=4

Answer 1

ln(x)+ln(y)=ln(xy)

Answer 2

ln[(2-x)(3x)]=4

Answer 3

to get rid of the natural log base e both sides

Answer 4

e^(ln[(2-x)(3x)]=e^4

Answer 5

so we have (2-x)(3x)=e^4

Answer 6

6x-3x^2-e^4=0

Answer 7

we can use the quadratic formula now!

Answer 8

since we have -3x^2+6x-e^4=0, we have a=-3, b=6, c=-e^4

Answer 9

so x=(-6 @ sqrt(36-4*(-3)*(-e^4)))/(-6) where @ symbolizes + or -

Answer 10

make sure your x is positve because you cannot have natural log of a negative number