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Simplifying Ln(x + 6) + -1ln(x + -4) = lnx Reorder the terms: nL(6 + x) + -1ln(x + -4) = lnx (6 * nL + x * nL) + -1ln(x + -4) = lnx (6nL + nxL) + -1ln(x + -4) = lnx Reorder the terms: 6nL + nxL + -1ln(-4 + x) = lnx 6nL + nxL + (-4 * -1ln + x * -1ln) = lnx 6nL + nxL + (4ln + -1lnx) = lnx Reorder the terms: 4ln + -1lnx + 6nL + nxL = lnx Solving 4ln + -1lnx + 6nL + nxL = 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. 4ln + -1lnx + 6nL + -1lnx + nxL = lnx + -1lnx Reorder the terms: 4ln + -1lnx + -1lnx + 6nL + nxL = lnx + -1lnx Combine like terms: -1lnx + -1lnx = -2lnx 4ln + -2lnx + 6nL + nxL = lnx + -1lnx Combine like terms: lnx + -1lnx = 0 4ln + -2lnx + 6nL + nxL = 0 Add '-6nL' to each side of the equation. 4ln + -2lnx + 6nL + -6nL + nxL = 0 + -6nL Combine like terms: 6nL + -6nL = 0 4ln + -2lnx + 0 + nxL = 0 + -6nL 4ln + -2lnx + nxL = 0 + -6nL Remove the zero: 4ln + -2lnx + nxL = -6nL Add '-1nxL' to each side of the equation. 4ln + -2lnx + nxL + -1nxL = -6nL + -1nxL Combine like terms: nxL + -1nxL = 0 4ln + -2lnx + 0 = -6nL + -1nxL 4ln + -2lnx = -6nL + -1nxL Reorder the terms: 4ln + -2lnx + 6nL + nxL = -6nL + 6nL + -1nxL + nxL Combine like terms: -6nL + 6nL = 0 4ln + -2lnx + 6nL + nxL = 0 + -1nxL + nxL 4ln + -2lnx + 6nL + nxL = -1nxL + nxL Combine like terms: -1nxL + nxL = 0 4ln + -2lnx + 6nL + nxL = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(4l + -2lx + 6L + xL) = 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 '(4l + -2lx + 6L + xL)' equal to zero and attempt to solve: Simplifying 4l + -2lx + 6L + xL = 0 Reorder the terms: 6L + 4l + -2lx + xL = 0 Solving 6L + 4l + -2lx + xL = 0 Move all terms containing l to the left, all other terms to the right. Add '-6L' to each side of the equation. 6L + 4l + -2lx + -6L + xL = 0 + -6L Reorder the terms: 6L + -6L + 4l + -2lx + xL = 0 + -6L Combine like terms: 6L + -6L = 0 0 + 4l + -2lx + xL = 0 + -6L 4l + -2lx + xL = 0 + -6L Remove the zero: 4l + -2lx + xL = -6L Add '-1xL' to each side of the equation. 4l + -2lx + xL + -1xL = -6L + -1xL Combine like terms: xL + -1xL = 0 4l + -2lx + 0 = -6L + -1xL 4l + -2lx = -6L + -1xL 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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