Ln(-x+1)-ln(3x+5)=ln(6x+1)

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Solution for Ln(-x+1)-ln(3x+5)=ln(6x+1) equation:


Simplifying
Ln(-1x + 1) + -1ln(3x + 5) = ln(6x + 1)

Reorder the terms:
nL(1 + -1x) + -1ln(3x + 5) = ln(6x + 1)
(1 * nL + -1x * nL) + -1ln(3x + 5) = ln(6x + 1)
(1nL + -1nxL) + -1ln(3x + 5) = ln(6x + 1)

Reorder the terms:
1nL + -1nxL + -1ln(5 + 3x) = ln(6x + 1)
1nL + -1nxL + (5 * -1ln + 3x * -1ln) = ln(6x + 1)
1nL + -1nxL + (-5ln + -3lnx) = ln(6x + 1)

Reorder the terms:
-5ln + -3lnx + 1nL + -1nxL = ln(6x + 1)

Reorder the terms:
-5ln + -3lnx + 1nL + -1nxL = ln(1 + 6x)
-5ln + -3lnx + 1nL + -1nxL = (1 * ln + 6x * ln)
-5ln + -3lnx + 1nL + -1nxL = (1ln + 6lnx)

Solving
-5ln + -3lnx + 1nL + -1nxL = 1ln + 6lnx

Solving for variable 'l'.

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

Add '-1ln' to each side of the equation.
-5ln + -3lnx + 1nL + -1ln + -1nxL = 1ln + -1ln + 6lnx

Reorder the terms:
-5ln + -1ln + -3lnx + 1nL + -1nxL = 1ln + -1ln + 6lnx

Combine like terms: -5ln + -1ln = -6ln
-6ln + -3lnx + 1nL + -1nxL = 1ln + -1ln + 6lnx

Combine like terms: 1ln + -1ln = 0
-6ln + -3lnx + 1nL + -1nxL = 0 + 6lnx
-6ln + -3lnx + 1nL + -1nxL = 6lnx

Add '-6lnx' to each side of the equation.
-6ln + -3lnx + 1nL + -6lnx + -1nxL = 6lnx + -6lnx

Reorder the terms:
-6ln + -3lnx + -6lnx + 1nL + -1nxL = 6lnx + -6lnx

Combine like terms: -3lnx + -6lnx = -9lnx
-6ln + -9lnx + 1nL + -1nxL = 6lnx + -6lnx

Combine like terms: 6lnx + -6lnx = 0
-6ln + -9lnx + 1nL + -1nxL = 0

Add '-1nL' to each side of the equation.
-6ln + -9lnx + 1nL + -1nL + -1nxL = 0 + -1nL

Combine like terms: 1nL + -1nL = 0
-6ln + -9lnx + 0 + -1nxL = 0 + -1nL
-6ln + -9lnx + -1nxL = 0 + -1nL
Remove the zero:
-6ln + -9lnx + -1nxL = -1nL

Add 'nxL' to each side of the equation.
-6ln + -9lnx + -1nxL + nxL = -1nL + nxL

Combine like terms: -1nxL + nxL = 0
-6ln + -9lnx + 0 = -1nL + nxL
-6ln + -9lnx = -1nL + nxL

Reorder the terms:
-6ln + -9lnx + nL + -1nxL = -1nL + nL + nxL + -1nxL

Combine like terms: -1nL + nL = 0
-6ln + -9lnx + nL + -1nxL = 0 + nxL + -1nxL
-6ln + -9lnx + nL + -1nxL = nxL + -1nxL

Combine like terms: nxL + -1nxL = 0
-6ln + -9lnx + nL + -1nxL = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(-6l + -9lx + L + -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 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 '(-6l + -9lx + L + -1xL)' equal to zero and attempt to solve: Simplifying -6l + -9lx + L + -1xL = 0 Reorder the terms: L + -6l + -9lx + -1xL = 0 Solving L + -6l + -9lx + -1xL = 0 Move all terms containing l to the left, all other terms to the right. Add '-1L' to each side of the equation. L + -6l + -9lx + -1L + -1xL = 0 + -1L Reorder the terms: L + -1L + -6l + -9lx + -1xL = 0 + -1L Combine like terms: L + -1L = 0 0 + -6l + -9lx + -1xL = 0 + -1L -6l + -9lx + -1xL = 0 + -1L Remove the zero: -6l + -9lx + -1xL = -1L Add 'xL' to each side of the equation. -6l + -9lx + -1xL + xL = -1L + xL Combine like terms: -1xL + xL = 0 -6l + -9lx + 0 = -1L + xL -6l + -9lx = -1L + xL 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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