ln(x)*(2-ln(x))=0

Solution for ln(x)*(2-ln(x))=0 equation:

Simplifying
ln(x)(2 + -1ln(x)) = 0

Multiply ln * x
ln * x(2 + -1lnx) = 0

Multiply ln * x
lnx(2 + -1lnx) = 0
(2 * lnx + -1lnx * lnx) = 0
(2lnx + -1l2n2x2) = 0

Solving
2lnx + -1l2n2x2 = 0

Solving for variable 'l'.

Factor out the Greatest Common Factor (GCF), 'lnx'.
lnx(2 + -1lnx) = 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 '(2 + -1lnx)' equal to zero and attempt to solve:

Simplifying
2 + -1lnx = 0

Solving
2 + -1lnx = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1lnx = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1lnx = 0 + -2
-1lnx = 0 + -2

Combine like terms: 0 + -2 = -2
-1lnx = -2

Divide each side by '-1nx'.
l = 2n-1x-1

Simplifying
l = 2n-1x-1
Solution
l = {2n-1x-1}