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Simplifying Ln(1 + -1x) + ln(6 + -1x) = ln(14) (1 * nL + -1x * nL) + ln(6 + -1x) = ln(14) (1nL + -1nxL) + ln(6 + -1x) = ln(14) 1nL + -1nxL + (6 * ln + -1x * ln) = ln(14) 1nL + -1nxL + (6ln + -1lnx) = ln(14) Reorder the terms: 6ln + -1lnx + 1nL + -1nxL = ln(14) Reorder the terms for easier multiplication: 6ln + -1lnx + 1nL + -1nxL = 14ln Solving 6ln + -1lnx + 1nL + -1nxL = 14ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-14ln' to each side of the equation. 6ln + -1lnx + 1nL + -14ln + -1nxL = 14ln + -14ln Reorder the terms: 6ln + -14ln + -1lnx + 1nL + -1nxL = 14ln + -14ln Combine like terms: 6ln + -14ln = -8ln -8ln + -1lnx + 1nL + -1nxL = 14ln + -14ln Combine like terms: 14ln + -14ln = 0 -8ln + -1lnx + 1nL + -1nxL = 0 Add '-1nL' to each side of the equation. -8ln + -1lnx + 1nL + -1nL + -1nxL = 0 + -1nL Combine like terms: 1nL + -1nL = 0 -8ln + -1lnx + 0 + -1nxL = 0 + -1nL -8ln + -1lnx + -1nxL = 0 + -1nL Remove the zero: -8ln + -1lnx + -1nxL = -1nL Add 'nxL' to each side of the equation. -8ln + -1lnx + -1nxL + nxL = -1nL + nxL Combine like terms: -1nxL + nxL = 0 -8ln + -1lnx + 0 = -1nL + nxL -8ln + -1lnx = -1nL + nxL Reorder the terms: -8ln + -1lnx + nL + -1nxL = -1nL + nL + nxL + -1nxL Combine like terms: -1nL + nL = 0 -8ln + -1lnx + nL + -1nxL = 0 + nxL + -1nxL -8ln + -1lnx + nL + -1nxL = nxL + -1nxL Combine like terms: nxL + -1nxL = 0 -8ln + -1lnx + nL + -1nxL = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(-8l + -1lx + 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 '(-8l + -1lx + L + -1xL)' equal to zero and attempt to solve: Simplifying -8l + -1lx + L + -1xL = 0 Reorder the terms: L + -8l + -1lx + -1xL = 0 Solving L + -8l + -1lx + -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 + -8l + -1lx + -1L + -1xL = 0 + -1L Reorder the terms: L + -1L + -8l + -1lx + -1xL = 0 + -1L Combine like terms: L + -1L = 0 0 + -8l + -1lx + -1xL = 0 + -1L -8l + -1lx + -1xL = 0 + -1L Remove the zero: -8l + -1lx + -1xL = -1L Add 'xL' to each side of the equation. -8l + -1lx + -1xL + xL = -1L + xL Combine like terms: -1xL + xL = 0 -8l + -1lx + 0 = -1L + xL -8l + -1lx = -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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