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

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


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

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

Solving
-1ln + 2lnx = 4ln + -1lnx

Solving for variable 'l'.

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

Add '-4ln' to each side of the equation.
-1ln + -4ln + 2lnx = 4ln + -4ln + -1lnx

Combine like terms: -1ln + -4ln = -5ln
-5ln + 2lnx = 4ln + -4ln + -1lnx

Combine like terms: 4ln + -4ln = 0
-5ln + 2lnx = 0 + -1lnx
-5ln + 2lnx = -1lnx

Add 'lnx' to each side of the equation.
-5ln + 2lnx + lnx = -1lnx + lnx

Combine like terms: 2lnx + lnx = 3lnx
-5ln + 3lnx = -1lnx + lnx

Combine like terms: -1lnx + lnx = 0
-5ln + 3lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-5 + 3x) = 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 '(-5 + 3x)' equal to zero and attempt to solve:

Simplifying
-5 + 3x = 0

Solving
-5 + 3x = 0

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

Add '5' to each side of the equation.
-5 + 5 + 3x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 3x = 0 + 5
3x = 0 + 5

Combine like terms: 0 + 5 = 5
3x = 5

Add '-3x' to each side of the equation.
3x + -3x = 5 + -3x

Combine like terms: 3x + -3x = 0
0 = 5 + -3x

Simplifying
0 = 5 + -3x

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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