Ln(3-x)=ln(1-2x)

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


Simplifying
Ln(3 + -1x) = ln(1 + -2x)
(3 * nL + -1x * nL) = ln(1 + -2x)
(3nL + -1nxL) = ln(1 + -2x)
3nL + -1nxL = (1 * ln + -2x * ln)
3nL + -1nxL = (1ln + -2lnx)

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

Solving for variable 'n'.

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

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

Reorder the terms:
-1ln + 3nL + -1nxL = 1ln + -1ln + -2lnx

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

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

Reorder the terms:
-1ln + 2lnx + 3nL + -1nxL = -2lnx + 2lnx

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

Factor out the Greatest Common Factor (GCF), 'n'.
n(-1l + 2lx + 3L + -1xL) = 0


Subproblem 1
Set the factor 'n' equal to zero and attempt to solve:

Simplifying
n = 0

Solving
n = 0

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

Simplifying
n = 0

Subproblem 2
Set the factor '(-1l + 2lx + 3L + -1xL)' equal to zero and attempt to solve:

Simplifying
-1l + 2lx + 3L + -1xL = 0

Reorder the terms:
3L + -1l + 2lx + -1xL = 0

Solving
3L + -1l + 2lx + -1xL = 0

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

Add '-3L' to each side of the equation.
3L + -1l + 2lx + -3L + -1xL = 0 + -3L

Reorder the terms:
3L + -3L + -1l + 2lx + -1xL = 0 + -3L

Combine like terms: 3L + -3L = 0
0 + -1l + 2lx + -1xL = 0 + -3L
-1l + 2lx + -1xL = 0 + -3L
Remove the zero:
-1l + 2lx + -1xL = -3L

Add 'l' to each side of the equation.
-1l + 2lx + l + -1xL = -3L + l

Reorder the terms:
-1l + l + 2lx + -1xL = -3L + l

Combine like terms: -1l + l = 0
0 + 2lx + -1xL = -3L + l
2lx + -1xL = -3L + l

Add '-2lx' to each side of the equation.
2lx + -2lx + -1xL = -3L + l + -2lx

Combine like terms: 2lx + -2lx = 0
0 + -1xL = -3L + l + -2lx
-1xL = -3L + l + -2lx

Add 'xL' to each side of the equation.
-1xL + xL = -3L + l + -2lx + xL

Combine like terms: -1xL + xL = 0
0 = -3L + l + -2lx + xL

Simplifying
0 = -3L + l + -2lx + xL

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
n = {0}

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