ln(x-1)=ln(2x)+ln(9)-2ln(3)

Solution for ln(x-1)=ln(2x)+ln(9)-2ln(3) equation:

Simplifying
ln(x + -1) = ln(2x) + ln(9) + -2ln(3)

Reorder the terms:
ln(-1 + x) = ln(2x) + ln(9) + -2ln(3)
(-1 * ln + x * ln) = ln(2x) + ln(9) + -2ln(3)
(-1ln + lnx) = ln(2x) + ln(9) + -2ln(3)

Remove parenthesis around (2x)
-1ln + lnx = ln * 2x + ln(9) + -2ln(3)

Reorder the terms for easier multiplication:
-1ln + lnx = 2ln * x + ln(9) + -2ln(3)

Multiply ln * x
-1ln + lnx = 2lnx + ln(9) + -2ln(3)

Reorder the terms for easier multiplication:
-1ln + lnx = 2lnx + 9ln + -2ln(3)

Reorder the terms for easier multiplication:
-1ln + lnx = 2lnx + 9ln + -2 * 3ln

Multiply -2 * 3
-1ln + lnx = 2lnx + 9ln + -6ln

Reorder the terms:
-1ln + lnx = 9ln + -6ln + 2lnx

Combine like terms: 9ln + -6ln = 3ln
-1ln + lnx = 3ln + 2lnx

Solving
-1ln + lnx = 3ln + 2lnx

Solving for variable 'l'.

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

Add '-3ln' to each side of the equation.
-1ln + -3ln + lnx = 3ln + -3ln + 2lnx

Combine like terms: -1ln + -3ln = -4ln
-4ln + lnx = 3ln + -3ln + 2lnx

Combine like terms: 3ln + -3ln = 0
-4ln + lnx = 0 + 2lnx
-4ln + lnx = 2lnx

Add '-2lnx' to each side of the equation.
-4ln + lnx + -2lnx = 2lnx + -2lnx

Combine like terms: lnx + -2lnx = -1lnx
-4ln + -1lnx = 2lnx + -2lnx

Combine like terms: 2lnx + -2lnx = 0
-4ln + -1lnx = 0

Factor out the Greatest Common Factor (GCF), '-1ln'.
-1ln(4 + x) = 0

Ignore the factor -1.
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 '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Add '-1x' to each side of the equation.
x + -1x = -4 + -1x

Combine like terms: x + -1x = 0
0 = -4 + -1x

Simplifying
0 = -4 + -1x

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.