2ln(x-1)-ln(x-4)=0

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Solution for 2ln(x-1)-ln(x-4)=0 equation: 


Simplifying
2ln(x + -1) + -1ln(x + -4) = 0

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

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

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

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

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

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

Simplifying
2 + x = 0

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

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

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

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

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

Simplifying
0 = -2 + -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.

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