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Simplifying Ln(x + -1) + ln(5 + -1x) = 0 Reorder the terms: nL(-1 + x) + ln(5 + -1x) = 0 (-1 * nL + x * nL) + ln(5 + -1x) = 0 (-1nL + nxL) + ln(5 + -1x) = 0 -1nL + nxL + (5 * ln + -1x * ln) = 0 -1nL + nxL + (5ln + -1lnx) = 0 Reorder the terms: 5ln + -1lnx + -1nL + nxL = 0 Solving 5ln + -1lnx + -1nL + nxL = 0 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add 'nL' to each side of the equation. 5ln + -1lnx + -1nL + nL + nxL = 0 + nL Combine like terms: -1nL + nL = 0 5ln + -1lnx + 0 + nxL = 0 + nL 5ln + -1lnx + nxL = 0 + nL Remove the zero: 5ln + -1lnx + nxL = nL Add '-1nxL' to each side of the equation. 5ln + -1lnx + nxL + -1nxL = nL + -1nxL Combine like terms: nxL + -1nxL = 0 5ln + -1lnx + 0 = nL + -1nxL 5ln + -1lnx = nL + -1nxL Reorder the terms: 5ln + -1lnx + -1nL + nxL = nL + -1nL + -1nxL + nxL Combine like terms: nL + -1nL = 0 5ln + -1lnx + -1nL + nxL = 0 + -1nxL + nxL 5ln + -1lnx + -1nL + nxL = -1nxL + nxL Combine like terms: -1nxL + nxL = 0 5ln + -1lnx + -1nL + nxL = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(5l + -1lx + -1L + 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 '(5l + -1lx + -1L + xL)' equal to zero and attempt to solve: Simplifying 5l + -1lx + -1L + xL = 0 Reorder the terms: -1L + 5l + -1lx + xL = 0 Solving -1L + 5l + -1lx + xL = 0 Move all terms containing l to the left, all other terms to the right. Add 'L' to each side of the equation. -1L + 5l + -1lx + L + xL = 0 + L Reorder the terms: -1L + L + 5l + -1lx + xL = 0 + L Combine like terms: -1L + L = 0 0 + 5l + -1lx + xL = 0 + L 5l + -1lx + xL = 0 + L Remove the zero: 5l + -1lx + xL = L Add '-1xL' to each side of the equation. 5l + -1lx + xL + -1xL = L + -1xL Combine like terms: xL + -1xL = 0 5l + -1lx + 0 = L + -1xL 5l + -1lx = L + -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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