ln(x)*(ln(x)-3)=0

Solution for ln(x)*(ln(x)-3)=0 equation:

Simplifying
ln(x)(ln(x) + -3) = 0

Multiply ln * x
ln * x(lnx + -3) = 0

Reorder the terms:
ln * x(-3 + lnx) = 0

Multiply ln * x
lnx(-3 + lnx) = 0
(-3 * lnx + lnx * lnx) = 0
(-3lnx + l2n2x2) = 0

Solving
-3lnx + l2n2x2 = 0

Solving for variable 'l'.

Factor out the Greatest Common Factor (GCF), 'lnx'.
lnx(-3 + lnx) = 0

Subproblem 1
Set the factor 'lnx' equal to zero and attempt to solve:

Simplifying
lnx = 0

Solving
lnx = 0

Move all terms containing l to the left, all other terms to the right.

Simplifying
lnx = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(-3 + lnx)' equal to zero and attempt to solve:

Simplifying
-3 + lnx = 0

Solving
-3 + lnx = 0

Move all terms containing l to the left, all other terms to the right.

Add '3' to each side of the equation.
-3 + 3 + lnx = 0 + 3

Combine like terms: -3 + 3 = 0
0 + lnx = 0 + 3
lnx = 0 + 3

Combine like terms: 0 + 3 = 3
lnx = 3

Divide each side by 'nx'.
l = 3n-1x-1

Simplifying
l = 3n-1x-1
Solution
l = {3n-1x-1}