ln(2x)*ln(6)=ln(x)

Solution for ln(2x)*ln(6)=ln(x) equation:

Simplifying
ln(2x) * ln(6) = ln(x)

Remove parenthesis around (2x)
ln * 2x * ln(6) = ln(x)

Reorder the terms for easier multiplication:
2 * 6ln * x * ln = ln(x)

Multiply 2 * 6
12ln * x * ln = ln(x)

Multiply ln * x
12lnx * ln = ln(x)

Multiply lnx * ln
12l2n2x = ln(x)

Multiply ln * x
12l2n2x = lnx

Solving
12l2n2x = lnx

Solving for variable 'l'.

Reorder the terms:
-1lnx + 12l2n2x = lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
-1lnx + 12l2n2x = 0

Factor out the Greatest Common Factor (GCF), 'lnx'.
lnx(-1 + 12ln) = 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 '(-1 + 12ln)' equal to zero and attempt to solve:

Simplifying
-1 + 12ln = 0

Solving
-1 + 12ln = 0

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

Add '1' to each side of the equation.
-1 + 1 + 12ln = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 12ln = 0 + 1
12ln = 0 + 1

Combine like terms: 0 + 1 = 1
12ln = 1

Divide each side by '12n'.
l = 0.08333333333n-1

Simplifying
l = 0.08333333333n-1
Solution
l = {0.08333333333n-1}