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

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Solution for ln(x-1)-2ln(x-2)=0 equation: 


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

Reorder the terms:
ln(-1 + x) + -2ln(x + -2) = 0
(-1 * ln + x * ln) + -2ln(x + -2) = 0
(-1ln + lnx) + -2ln(x + -2) = 0

Reorder the terms:
-1ln + lnx + -2ln(-2 + x) = 0
-1ln + lnx + (-2 * -2ln + x * -2ln) = 0
-1ln + lnx + (4ln + -2lnx) = 0

Reorder the terms:
-1ln + 4ln + lnx + -2lnx = 0

Combine like terms: -1ln + 4ln = 3ln
3ln + lnx + -2lnx = 0

Combine like terms: lnx + -2lnx = -1lnx
3ln + -1lnx = 0

Solving
3ln + -1lnx = 0

Solving for variable 'l'.

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

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(3 + -1x) = 0


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 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Add 'x' to each side of the equation.
-1x + x = -3 + x

Combine like terms: -1x + x = 0
0 = -3 + x

Simplifying
0 = -3 + x

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.

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