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Simplifying Ln(x + 4) + -1ln(x + -10) = ln(8) Reorder the terms: nL(4 + x) + -1ln(x + -10) = ln(8) (4 * nL + x * nL) + -1ln(x + -10) = ln(8) (4nL + nxL) + -1ln(x + -10) = ln(8) Reorder the terms: 4nL + nxL + -1ln(-10 + x) = ln(8) 4nL + nxL + (-10 * -1ln + x * -1ln) = ln(8) 4nL + nxL + (10ln + -1lnx) = ln(8) Reorder the terms: 10ln + -1lnx + 4nL + nxL = ln(8) Reorder the terms for easier multiplication: 10ln + -1lnx + 4nL + nxL = 8ln Solving 10ln + -1lnx + 4nL + nxL = 8ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-8ln' to each side of the equation. 10ln + -1lnx + 4nL + -8ln + nxL = 8ln + -8ln Reorder the terms: 10ln + -8ln + -1lnx + 4nL + nxL = 8ln + -8ln Combine like terms: 10ln + -8ln = 2ln 2ln + -1lnx + 4nL + nxL = 8ln + -8ln Combine like terms: 8ln + -8ln = 0 2ln + -1lnx + 4nL + nxL = 0 Add '-4nL' to each side of the equation. 2ln + -1lnx + 4nL + -4nL + nxL = 0 + -4nL Combine like terms: 4nL + -4nL = 0 2ln + -1lnx + 0 + nxL = 0 + -4nL 2ln + -1lnx + nxL = 0 + -4nL Remove the zero: 2ln + -1lnx + nxL = -4nL Add '-1nxL' to each side of the equation. 2ln + -1lnx + nxL + -1nxL = -4nL + -1nxL Combine like terms: nxL + -1nxL = 0 2ln + -1lnx + 0 = -4nL + -1nxL 2ln + -1lnx = -4nL + -1nxL Reorder the terms: 2ln + -1lnx + 4nL + nxL = -4nL + 4nL + -1nxL + nxL Combine like terms: -4nL + 4nL = 0 2ln + -1lnx + 4nL + nxL = 0 + -1nxL + nxL 2ln + -1lnx + 4nL + nxL = -1nxL + nxL Combine like terms: -1nxL + nxL = 0 2ln + -1lnx + 4nL + nxL = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(2l + -1lx + 4L + 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 '(2l + -1lx + 4L + xL)' equal to zero and attempt to solve: Simplifying 2l + -1lx + 4L + xL = 0 Reorder the terms: 4L + 2l + -1lx + xL = 0 Solving 4L + 2l + -1lx + xL = 0 Move all terms containing l to the left, all other terms to the right. Add '-4L' to each side of the equation. 4L + 2l + -1lx + -4L + xL = 0 + -4L Reorder the terms: 4L + -4L + 2l + -1lx + xL = 0 + -4L Combine like terms: 4L + -4L = 0 0 + 2l + -1lx + xL = 0 + -4L 2l + -1lx + xL = 0 + -4L Remove the zero: 2l + -1lx + xL = -4L Add '-1xL' to each side of the equation. 2l + -1lx + xL + -1xL = -4L + -1xL Combine like terms: xL + -1xL = 0 2l + -1lx + 0 = -4L + -1xL 2l + -1lx = -4L + -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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