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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 = 3lnx -6ln + 3lnx + 1nL + -1nxL = -6lnx + 6lnx Combine like terms: -6lnx + 6lnx = 0 -6ln + 3lnx + 1nL + -1nxL = 0 Add '-1nL' to each side of the equation. -6ln + 3lnx + 1nL + -1nL + -1nxL = 0 + -1nL Combine like terms: 1nL + -1nL = 0 -6ln + 3lnx + 0 + -1nxL = 0 + -1nL -6ln + 3lnx + -1nxL = 0 + -1nL Remove the zero: -6ln + 3lnx + -1nxL = -1nL Add 'nxL' to each side of the equation. -6ln + 3lnx + -1nxL + nxL = -1nL + nxL Combine like terms: -1nxL + nxL = 0 -6ln + 3lnx + 0 = -1nL + nxL -6ln + 3lnx = -1nL + nxL Reorder the terms: -6ln + 3lnx + nL + -1nxL = -1nL + nL + nxL + -1nxL Combine like terms: -1nL + nL = 0 -6ln + 3lnx + nL + -1nxL = 0 + nxL + -1nxL -6ln + 3lnx + nL + -1nxL = nxL + -1nxL Combine like terms: nxL + -1nxL = 0 -6ln + 3lnx + nL + -1nxL = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(-6l + 3lx + L + -1xL) = 0Subproblem 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 + 3lx + L + -1xL)' equal to zero and attempt to solve: Simplifying -6l + 3lx + L + -1xL = 0 Reorder the terms: L + -6l + 3lx + -1xL = 0 Solving L + -6l + 3lx + -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 + 3lx + -1L + -1xL = 0 + -1L Reorder the terms: L + -1L + -6l + 3lx + -1xL = 0 + -1L Combine like terms: L + -1L = 0 0 + -6l + 3lx + -1xL = 0 + -1L -6l + 3lx + -1xL = 0 + -1L Remove the zero: -6l + 3lx + -1xL = -1L Add 'xL' to each side of the equation. -6l + 3lx + -1xL + xL = -1L + xL Combine like terms: -1xL + xL = 0 -6l + 3lx + 0 = -1L + xL -6l + 3lx = -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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