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

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


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

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

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

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

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

Solving for variable 'l'.

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

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

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

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

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

Add '2nL' to each side of the equation.
1ln + -2lnx + -2nL + 2nL + 2nxL = 0 + 2nL

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

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

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

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

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

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

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

Subproblem 1

Set the factor 'n' equal to zero and attempt to solve: Simplifying n = 0 Solving n = 0 Move all terms containing l to the left, all other terms to the right. Add '-1n' to each side of the equation. n + -1n = 0 + -1n Remove the zero: 0 = -1n Simplifying 0 = -1n 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 '(l + -2lx + -2L + 2xL)' equal to zero and attempt to solve: Simplifying l + -2lx + -2L + 2xL = 0 Reorder the terms: -2L + l + -2lx + 2xL = 0 Solving -2L + l + -2lx + 2xL = 0 Move all terms containing l to the left, all other terms to the right. Add '2L' to each side of the equation. -2L + l + -2lx + 2L + 2xL = 0 + 2L Reorder the terms: -2L + 2L + l + -2lx + 2xL = 0 + 2L Combine like terms: -2L + 2L = 0 0 + l + -2lx + 2xL = 0 + 2L l + -2lx + 2xL = 0 + 2L Remove the zero: l + -2lx + 2xL = 2L Add '-2xL' to each side of the equation. l + -2lx + 2xL + -2xL = 2L + -2xL Combine like terms: 2xL + -2xL = 0 l + -2lx + 0 = 2L + -2xL l + -2lx = 2L + -2xL 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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