ln(x)+ln(x-6)=ln(6x)

Solution for ln(x)+ln(x-6)=ln(6x) equation:

Simplifying
ln(x) + ln(x + -6) = ln(6x)

Multiply ln * x
lnx + ln(x + -6) = ln(6x)

Reorder the terms:
lnx + ln(-6 + x) = ln(6x)
lnx + (-6 * ln + x * ln) = ln(6x)
lnx + (-6ln + lnx) = ln(6x)

Reorder the terms:
-6ln + lnx + lnx = ln(6x)

Combine like terms: lnx + lnx = 2lnx
-6ln + 2lnx = ln(6x)

Remove parenthesis around (6x)
-6ln + 2lnx = ln * 6x

Reorder the terms for easier multiplication:
-6ln + 2lnx = 6ln * x

Multiply ln * x
-6ln + 2lnx = 6lnx

Solving
-6ln + 2lnx = 6lnx

Solving for variable 'l'.

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

Add '-6lnx' to each side of the equation.
-6ln + 2lnx + -6lnx = 6lnx + -6lnx

Combine like terms: 2lnx + -6lnx = -4lnx
-6ln + -4lnx = 6lnx + -6lnx

Combine like terms: 6lnx + -6lnx = 0
-6ln + -4lnx = 0

Factor out the Greatest Common Factor (GCF), '-2ln'.
-2ln(3 + 2x) = 0

Ignore the factor -2.
Subproblem 1
Set the factor 'ln' equal to zero and attempt to solve:

Simplifying
ln = 0

Solving
ln = 0

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

Simplifying
ln = 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 + 2x)' equal to zero and attempt to solve:

Simplifying
3 + 2x = 0

Solving
3 + 2x = 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 + 2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2x = 0 + -3
2x = 0 + -3

Combine like terms: 0 + -3 = -3
2x = -3

Add '-2x' to each side of the equation.
2x + -2x = -3 + -2x

Combine like terms: 2x + -2x = 0
0 = -3 + -2x

Simplifying
0 = -3 + -2x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.