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

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

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

Reorder the terms:
nL(-2 + x) = ln(2x + -1)
(-2 * nL + x * nL) = ln(2x + -1)
(-2nL + nxL) = ln(2x + -1)

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

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

Solving for variable 'n'.

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

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

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

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

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

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

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

Factor out the Greatest Common Factor (GCF), 'n'.
n(l + -2lx + -2L + xL) = 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 '(l + -2lx + -2L + xL)' equal to zero and attempt to solve:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

The solution to this equation could not be determined.

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